Much quicker and easier to just treat 5^11 as 5^4 x 5^4 x 5^3, which is 625 x 625 x 125. Multiply 625 x 625 and then multiply that product by 125. Then subtract 9. This is much faster than the method shown.
After puzzling over this, the simplest solution seemed to me to be E = ((5^5)^2)*5 - 9; 5^5=3,125; so by long multiplication 3,125*3,125 = 9,765,625 then 9,765,625 * 5 = 48,828,125, and finally 48,828,125 - 9 = 48,828,116; or written out using segmentation and group multiplication, 3,125 * 3,125 = 3,000 * 3,125 + 100 * 3,125 + 20 *3,125 + 5 * 3,125 =9,765,625
Multiplying by 5 is pretty much the same as dividing by 2, just ignore the decimal point. This is how I would solve it: 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 - 9 48828116
10**11/2**11 would really be faster to obtain using long division. also during the solution it would be useful to remember that 24+26=50 and 24*26=(25-1)*(25+1)=25**2-1
I would just do: 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 48,828,125 3 x 3 = 9 48,828,125 - 9 = 48,828,116 So the answer is 48,828,116. I would of course do this all on paper by hand since no calculators are allowed. There’s no reason whatsoever to make it complicated, it’s as easy as that.
Wow. When I saw all the bases and exponents were different prime numbers, I didn't see where to start, though of course was looking for x^2 -- y^2 somewhere. This was great.
Was the intent to solve the question in the hardest way possible? I can devise a harder solution then yours. How about changing the numbers to base 17 before calculating...
@@hamzagezici1731 thank you. 10^3/2^4 is a very useful ratio to avoid long division by 2048. and indeed, 10^11/2^4 = 5^4*10^7 which is then easier to divide by 2^7
So, you did not ask for simplification but for a number. As, in any case you did long multiplication, it would have been faster to do a = 625 * 625 * 125 - 9
Notice that there is a mistake in calculations. After factoring out 5 and applying the rule of two squares equals sum times difference of squared numbers, you forgot to put it in square brackets. As a consequence you only multiply the first addend of the sum. Please correct me if I am wrong.
I guess that professors in mathematics from Stanford University, learned at secondary school already in "calculator era". So, they probably do not know about multiplication in column method.
It’s all about logic and problem-solving, not just calculation methods. 👍This problem tests your understanding of concepts, not your calculator skills 😎💯💕🙏
@@superacademy247 Excuse me, if multiplication in column works here faster, let say, it is not the best example of the problem. Should be common sense anyway. And, by the way, how did you get 5^5 so quickly?
Here's what I did: 5¹¹-3²=5³5⁸-3²=5³(5⁸-3²)+5³3²-3²=5³(5⁴+3)(5⁴-3)+5(5²3²)-3²=125(625+3)(625-3)+5(15²)-9 =(1000/8)(628)(622)+5(225)-9=(1000)(628/4)(622/2)+1125-9=(1000)(157)(311)+1116 =(1000)(48827)+1116=48827000+1116=48828116
I can't see any reason to calculate like this, just calculate 5 by 5, 5^2=25, 5^4=625, 5^5=3125, 5^10 = (3100+25)^2= 3100^2+2*3100*25+25^2=9610000+155000+625=9765625, then multiply by 5 and minus 9. multi-power of 5 should be an easy calculation, the method here is just nonsense.
For most of the commentators: this kind of exercise is for testing the imagination, beligerancy and resiliency of the candidate. So, congratulations, most of you would have passed the test. 😄
in english the letter "b" is pronounced as in "baby" not as in "papa" ... quite distracting also "a*b" is not read as "a into b" - rather "a times b" ... quite distracting
I like your solution too. 5^5=5*25^2=5*625=3125 Next, use a trick for squaring numbers that end in 5 5^10=3125^2=(300+12)(300+13)100+25=(90000+7500+156)100+25=9765625 5^11=5*5^10=97656250/2=48828125
Much quicker and easier to just treat 5^11 as 5^4 x 5^4 x 5^3, which is 625 x 625 x 125. Multiply 625 x 625 and then multiply that product by 125. Then subtract 9. This is much faster than the method shown.
Your last sentence is redundant.
Yes, calculating 5^11 by hand is indeed quite easy
An easier way to handle a number x 125 is to multiply the number by 1000 and then divide the result by 8. E.g. 496 x 125 =496000 ÷ 8 =....
625^2=(62×63)25=>
62x63=60^2+60+61+61+62+62=3906=>
625^2=390625
390625×125=390625×1000÷8
390625000÷8=48828125
5^11 - 9=48828125-9=48828116
Video is much more "simplified" as per ask
Takes less time to just multiply out the numbers.
Thank you! I did it in at most 3 minutes.
Exactly, I was gonna say that, too
Great lesson is the variety of techniques available in solving these types of problems. Thank you!
After puzzling over this, the simplest solution seemed to me to be E = ((5^5)^2)*5 - 9; 5^5=3,125; so by long multiplication 3,125*3,125 = 9,765,625 then 9,765,625 * 5 = 48,828,125, and finally 48,828,125 - 9 = 48,828,116; or written out using segmentation and group multiplication, 3,125 * 3,125 = 3,000 * 3,125 + 100 * 3,125 + 20 *3,125 + 5 * 3,125 =9,765,625
Wow! ✅
Multiplying by 5 is pretty much the same as dividing by 2, just ignore the decimal point. This is how I would solve it:
5
25
125
625
3125
15625
78125
390625
1953125
9765625
48828125 - 9
48828116
wow.
That's genius!
Riduculous. Making a meal of an extremely simple problem.
Explains why Stanford is down the tubes?
They are woke and ElGeeBeeTeaWue.
@@dalepeters4927
Indeed
5 x 3125 x 3125 - 9 is just as simple as 5 x 3126 x 3124 - 4, without the unnecessary steps of the first 4 minutes.
There is no one best way to do this problem. But with no calculator, I chose 100,000,000,00 ÷ 2048 - 9
your power of ten has 10 zeros while it should have 11
10**11/2**11 would really be faster to obtain using long division.
also during the solution it would be useful to remember that 24+26=50 and 24*26=(25-1)*(25+1)=25**2-1
I appreciate you watching! 👍💯Thanks for the feedback! 💕🥰✅Thanks for sharing your solution! 💯🙏🔥
I liked his way. It shows he knows algebra thoroughly. I'm sure Stanford has more difficult variations of the same problem.
I'm glad you found it helpful! 🤩💯Thanks for the feedback! 👍💯
Totally agree with everyone else. Much quicker and easier to just multiply the numbers out from the word go.
I would just do:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 48,828,125
3 x 3 = 9
48,828,125 - 9 = 48,828,116
So the answer is 48,828,116.
I would of course do this all on paper by hand since no calculators are allowed. There’s no reason whatsoever to make it complicated, it’s as easy as that.
5¹¹=5•5•5•5•5•5•5•5•5•5•5 ??? 😳
5¹¹=(10/2)¹¹=10¹¹/2¹¹=
=10¹¹/2/2/2/2/2/2/2/2/2/2/2 😁
Good practice.
😍✅
Nice information
Thanks 🤩
Wow. When I saw all the bases and exponents were different prime numbers, I didn't see where to start, though of course was looking for x^2 -- y^2 somewhere.
This was great.
Thanks for your positive vibe🤩🤩🤩
Imprezionante.
Was the intent to solve the question in the hardest way possible? I can devise a harder solution then yours. How about changing the numbers to base 17 before calculating...
Stanford University Admission Simplification Problem: 5¹¹ - 3² =?
5¹¹ = (5²)(5³)³ = (25)(5³)(5³)² = (25)(125)(125²)
125² = (10² + 25)² = 10⁴ + 5(10³) + 25² = 10⁴ + 5(10³) + 625 = 10⁴ + 5(10³) + 6(10²) + 25
5[10⁴ + 5(10³) + 6(10²) + 20 + 5] = 5(10⁴) + 25(10³) + 30(10²) + 10² + 25
= 7(10⁴) + 8(10³) + 10² + 25
5[7(10⁴) + 8(10³) + 10² + 25] = 35(10⁴) + 40(10³) + 5(10²) + 10² + 25
= 39(10⁴) + 5(10²) + 10² + 25 = 3(10⁵) + 9(10⁴) + 6(10²) + 25
5[3(10⁵) + 9(10⁴) + 6(10²) + 25] = 15(10⁵) + 45(10⁴) + 30(10²) + 10² + 25
= 10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25
(125)(125²) = 10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25
(25)(125)(125²) = (20 + 5)[10⁶ + 9(10⁵) + 5(10⁴) + 3(10³) + 10² + 25]
= 20(10⁶) + 180(10⁵) + 100(10⁴) + 60(10³) + 20(10²) + 500
+ 5(10⁶) + 45(10⁵) + 25(10⁴) + 15(10³) + 5(10²) + 125
= 25(10⁶) + 225(10⁵) + 125(10⁴) + 75(10³) + 25(10²) + 625
= 25(10⁶) + [22(10⁶) + 5(10⁵)] + [10⁶ + 2(10⁵) + 5(10⁴)] + [7(10⁴) + 5(10³)] + 3125
= 48(10⁶) + 7(10⁵) + 12(10⁴) + 5(10³) + 3(10³) + 10² + 25
= 4(10⁷) + 8(10⁶) + 8(10⁵) + 2(10⁴) + 8(10³) + 10² + 25 = 48828125
5¹¹ - 3² = 48828125 - 9 = 48828116
Great 👌 process. Nice 👍 solution.✅
Nice solution but too long . There are shorter ways.
10^11÷2^11-9
1000÷16=62.5
10^8×62.5=6250000000
6250000000÷128=4882825
48882825-9=48828116
@@hamzagezici1731 thank you. 10^3/2^4 is a very useful ratio to avoid long division by 2048. and indeed, 10^11/2^4 = 5^4*10^7 which is then easier to divide by 2^7
3125×3125×5-9，i think this is more easier. 😂😂
Easier is multiply eleven times the number 5 and then subtract 9 😂
This video is not about solving the equation, it is teaching us how to make a long form video with simple maths problem 😂
I appreciate your perspective! 🤩Thanks for your feedback! 💯😎
@ just kidding ya lol😂
What's the meaning teaching calculating?
It's not simple. Just calculating 5^11 is much more simple, easier and faster.
It's all about simplifying the expression and finding a clever way to represent it.✅💖😊😍
इतने समय में तो साधारण तरीके से भी सरल किया जा सकता है।
Its get long job well done the baby is crying 😂
5^11 - 3^2 = 25(125^3) - 9
125 x 125 = 12500 + 2500 + 625 = 15625
125^3 = 15625 x 125 = 1562500 + 312500 + 78125 = 1953125
25(125^3) = (125^3)(100)/4 = 195312500/4 = 48828125
5^11 - 3^2 = 48828125 - 9 = 48828116
So, you did not ask for simplification but for a number. As, in any case you did long multiplication, it would have been faster to do a = 625 * 625 * 125 - 9
Oh I would not consider of Stanford University if calculate by such method 😂
too many unnecessary steps. confusing the students.
Notice that there is a mistake in calculations. After factoring out 5 and applying the rule of two squares equals sum times difference of squared numbers, you forgot to put it in square brackets. As a consequence you only multiply the first addend of the sum.
Please correct me if I am wrong.
5x2(3126x1562)-4=10x(3126x1000+3126x562)-4,then 3126x562 can be easier to caculate
5^11 - 3^2 = 5^5 * 5^6 - 9
5^5 = 5^4 * 5 = 625 * 5 = 3,125
5^6 = 5^5 * 5 = 3125 * 5 = 15,625
3125 * 15,625 - 9 = 48,828,125 - 9 = 48,828,116 ... ok, might need a pencil to do this multiply
I guess that professors in mathematics from Stanford University, learned at secondary school already in "calculator era".
So, they probably do not know about multiplication in column method.
It’s all about logic and problem-solving, not just calculation methods. 👍This problem tests your understanding of concepts, not your calculator skills 😎💯💕🙏
@@superacademy247 Excuse me, if multiplication in column works here faster, let say, it is not the best example of the problem. Should be common sense anyway. And, by the way, how did you get 5^5 so quickly?
5^5 I got it quickly through experience because I'm exposed to numbers daily.
Crazy, on his video he says "no calculations allowed", yet all he is doing is calculations 😂
Here's what I did:
5¹¹-3²=5³5⁸-3²=5³(5⁸-3²)+5³3²-3²=5³(5⁴+3)(5⁴-3)+5(5²3²)-3²=125(625+3)(625-3)+5(15²)-9
=(1000/8)(628)(622)+5(225)-9=(1000)(628/4)(622/2)+1125-9=(1000)(157)(311)+1116
=(1000)(48827)+1116=48827000+1116=48828116
Awesome 😎💯
Let him show you how to make an easy one to complicated
Just do 3125x3125, one hundred of passages to NOT semplify a multiplication
I can't see any reason to calculate like this, just calculate 5 by 5, 5^2=25, 5^4=625, 5^5=3125, 5^10 = (3100+25)^2= 3100^2+2*3100*25+25^2=9610000+155000+625=9765625, then multiply by 5 and minus 9. multi-power of 5 should be an easy calculation, the method here is just nonsense.
The explanation categorizes this as an "algebra problem". Wrong, it is purely arithmetic, not algebraic, since there are no variables present.
😊
🤩
Chisanbop that jawn
Method 1
------------------
x= 5¹¹ - 3²; u=5¹¹ et v=3²
u=5¹¹
u=5³(5⁸)
u=(125)(5⁴)²
u=(100+25)(625)²
u=(10²+25)(600+25)²; a=25
u=(10²+a)(10²6+a)²; b=(10²6+a)²
u=(10²+a)b
/////////////////////////////////////////////////
b=(10²6+a)²
b=10⁴36+2(10²6)(25)+a²
b=10⁴36+(10²6)(10¹5)+a²
b=10⁴36+10⁴3+a²
b=10⁴(36+3)+a²
b=10⁴39+a²
//////////////////////////////////////////////////
u=(10²+a)b
u=(10²+a)(10⁴39+a²)
u=10⁶39+10²a²+10⁴39a+a³
u=10⁶39+10⁴39a+10²a²+a³
u=10⁶39+10⁴39(25)+10²a²+a³
u=10⁶39+10⁴(40-1)25+10²a²+a³
u=10⁶39+10⁴(10³-25)+10²(25)²+a³
u=10⁶39+10⁴(975)+10²(625)+a³
///////////////////////////////////////////////////
a³=a²a=25²25=(625)(25)=(600+a)a
=>a³=10²6a+a²=10²3(2a)+625
=>a³=10²3(50)+625
=>a³=10³15+625
=>a³=15'625
/////////////////////////////////////////////////
u=10⁶39+10⁴975+10²625+15'625
u=39'000'000+9'750'000+10²625+15'625
u=48'750'000+62'500+15'625
u=48'812'500+15'625
u=48'828'125
and
v=3² => v=9
Then,
x=u - v
x=48'828'125 - 9
Therefore,
x=48'828'116
Method 2
------------------
x=5¹¹ - 3²; u=5¹¹ et v=3²
u=5¹¹
log(u)=log(5)¹¹
log(u)=11log5; log5 ≈ 0,7
log(u)≈11(0,7)
log(u)≈7(1,1)
log(u)≈7,7; 7u>10⁷
u≈10⁷[10^(0,7)];
log5≈0,7 10^(0,7)≈5
u≈10⁷5
and
v=3² => v=9
then,
x= u -v
x≈ 10⁷5 -9
x≈ 50'000'000 -9
x≈ 49'999'991
Method 3
----------------
x= 5¹¹ - 3²; u=5¹¹ et v=3² (v= 9)
u=5¹¹
table 5ⁿ
n=1 ---> 5
n=2. ---> 25
n=3. ---> 125
4. 625
5. 3125
6. 15625
7. 78125
8. 390625
9. 1953125
10. 9765625
11. 48828125
=> u=48'828'125
then,
x= u -v
x= 48'828'125 - 9
therefore,
☆ x= 48'828'116
Unusually Very long procedure.
Is it really a admition test question ?!😮
no way this is an admission test, too difficult for most students
This was an actual problem in Stanford's admission test back in 2020 😂.
@@superacademy247which is a shame
自以為聰明，其實在繞遠路
For most of the commentators: this kind of exercise is for testing the imagination, beligerancy and resiliency of the candidate.
So, congratulations, most of you would have passed the test. 😄
Well said! Great point!
without calculator
5^11= 10^11/2^11= 5x10^10/2^10=25x10^9/2^9=125x10^8/2^8=625x10^7/2^7=3125x10^6/2^6=15625x10^5/2^5=78125x10^4/2^4
=390625x10^3/2^3=1953125x10^2/2^2=9765625X10/2=97656250/2=48828125
5^11-3^1=48828125-10+1=48828116
you just multiplied all fives sequentially which is not overly optimal unless you know higher powers of 5 by heart
3^2=9
It’s in my head
That's nice to know bro.
Is phoning a friend allowed for standird admission test ?
Given that 5=10/2,everything else is trivial
5^11 is only an 8-digit number, most calculator can do it.
Just multiply the numbers and subtract, it seems faster than the method here
Amerucan universities do not have enterance exams. Good and challenging problems but not an enterance exam.
5^11-3^2= 11-2=9
There is an admission test for Stanford?
It's a hypothetical problem based on the general admission process 😊It's a fun challenge, not a real Stanford test! 😅
You didn’t simplify anything, just a not easy way to calculate the numbers. While the original problem is also kind of stupid!
49
"Ridiculous" is a charitable assessment. "Tortured pointlessness" might be closer to it. What a waste.
Stanford admissions does not test math. Just submit your application.
Thanks for your comment! 🙏💕🥰✅That's an interesting perspective! 😎🥰✅
😊😊😊😊😊, THE SOLVED AS YOUR COUNTING , HOW IS IT FOR UNIVERSITY?!😊
in english the letter "b" is pronounced as in "baby" not as in "papa" ... quite distracting
also "a*b" is not read as "a into b" - rather "a times b" ... quite distracting
They drag out the solution which is torture for those of us interested in the problem.
I didn't know you had to solve such stupid questions in this university. Thanks. I won't apply for admission now.
Thanks for your feedback! 💖💯I’m glad you found it helpful! 🔥 💯
I like your solution too.
5^5=5*25^2=5*625=3125
Next, use a trick for squaring numbers that end in 5
5^10=3125^2=(300+12)(300+13)100+25=(90000+7500+156)100+25=9765625
5^11=5*5^10=97656250/2=48828125
Great 👌 trick.🙏🙏🙏
Décomposition en base 10 vow
Why so complicated ？ You won’t pass the test if you spend so much time solving this simple question.
Boring: 625x625x125-9=
Lol..classic example of how to overcomplicate a problem!!
Can it be so easy? Stanford seemed nerfed.
Seems complicated than just multiply the numbers haha
I don't think they didn't know that one can multiply numbers out. They want to know that ome is able to manipulate such equations.
5 * 5 * 5 * 5 *5 = 3125 not calculator allowed 😂😂🤣🤣
?
312 * 313 =97,656
5^10 =97,65,625
(Just add 25 in end )
97656250/2 =4,88,28,125
This is 5^11
5^11 = 5⁴ × 5⁴ × 5³ =
=(1000(100(62×63) + 25))/8
=390625000/8 = 48828125
So, 5^11-9 = 48828125-9=48828116
Not a nice solution.
How about using a LOG?
Why do you have to make it complecsted.
5^11=625*625*125= ((62*63*100)+25)*1000/8 =390625000/8=
48828125
(5^11)-9=48828116
이정도 문제는 한국에서는 중학교 3학년(미국에서 9학년) 수준 문제이다.
( 3125X3125X5 ) -9 = 48,828,116
Todo esto es perder el tiempo ... entonces para que se inventaron las calculadoras...?
This seems…awful? Easer to just multiply it out.
i get loose too long
rối rắm, quá chậm, cần lấy 5^5. 5^5. 5 là xong
Задача 9 класса Советской Школы.
Porque siempre se copia el enunciado otra vez?
Which statement?
그냥 계산하는 것이 빠르겠다
No calculation ???
use a calculator! no need to spend that much time
4,999,991?
ㅋㅋㅋ
Un calcul direct va encore plus vite. C'est stupide comme question.
Not satisfied
계산기로 그냥 11번 곱하는게 빠르겠다 ㅡㅡ
It seems not best answer
5^5=3125
3125*3125=9765625
9765625*5=48828125
48828125-9=48828116
3125^2
=(3000+125)^2
=9000000+750000+10000+5000+625
=9765625
Un proceso totalmente inútil, cuando lo más rápido y facil era hacer las multiplicaciones.
I appreciate your feedback! 💯🙏
Show-off video with many innecessary steps
this takes 5^10 times more time, got get a life man, one can solve 5^2 more problems in the same amount of time.
5^10*5-5-4=5(5^10-4)