(3 to the neg 1 divided by 3 to the neg 2) all over 3 x 3 squared =? MANY will get WRONG!
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- Опубліковано 24 тра 2024
- How to simplify a fraction with powers and exponents. Learn more math at TCMathAcademy.com/.
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Here the numerator works out to be 3. The denominator works out to be 27. You divide 3 by 27 or 1 by 9, as it is the same thing, and you reach your happiness easy with no stress. 0.111……
I like the way you teach maths. I wish I had a teacher like you back in the days.
Red black, what was wrong with your teacher. You did not pay attention in class now you blame your teacher. John is using modern technology your teacher did not even have a calculator. Think before you open your mouth. This man talks too much
yeah, I am guessing by your comment the multiple choice aspect? Because otherwise I guess maybe that is an American thing? (We very rarely have multiple choice in math and if we do you have to show it line by line nothing in your head and if there is a step missing on paper or you showed a multiplication sign instead of an X variable, but you knew in your head what it was... guess what, it is wrong. No such thing as partially right answers)
@@harrymatabal8448 After reading your comment, I think that my teacher was a much better teacher than you. We can always find worse. No calculators in my days. We used slide rules. I like John's style. What's wrong with you? Your mommy didn't give you enough affection?🤣
@@bigdog3628 No, It is not the multiple choice aspect. I was making reference to a math teacher that I had when I was in the 12th grade. She was very bad at explaining. That made things difficult. I think that John's explanations are great. I like his style. Later I had really great teachers when I was studying aeronautical engineering. Good teachers make a difference.
I simply subtracted the exponents in the numerator to get 3 and mentally calculated the denominator to get 27. Then reduced.
That makes too much sense. LOL!
That's how I did it (in my head).
@@joseeoliviero6078 I wish I had thought of it.
I converted the negative exponents to fractions, then flipped the one to multiply instead of divide.
Delighted to make your "likes" total an even 50! And thanks for this presentation; my days as a math major are long gone, and exponents appear to be an area that has faded into oblivion in my world. But, thanks to your videos, I now normally get the right answer.
Thank you!
As always great video, thanks!
three parts:
1:) Top is (1/3)9 which is 3. (first number is flipped due to the negative exponent, second number isn't but ONLY because it is a division as well as a negative exponent. x divided by Y is the same as x times 1 over y)
2:) Bottom is 3x9 which is 27 (you square the second 3 before multiplying by the first 3)
3:) Final step take the 3 from step one and the reciprocal of 27 from step 2. Which is then 3(1/27) which then equals (1/9) or choice D as it is multiple choice.
in the length of time it took to type all this I was able to do the problem in my head 30 times. I am a slow typer though.
Excellent marcus. The 3 in the numerator cancel 3 in denominator.
Even easier using the power rule & changing the top half to multiplication 3^-1 x 3^2 = 3.
Then you can easily see that 3 cancelling with 3 on the bottom leaving you with 1/3^2 (the answer)
Olivier excellent idea. Far better than this man who loves to talk
Numerator: 3^(-1) / 3^(-2) = 3² / 3¹ = 3 and denominator: 3 x 3² = 27 so the fraction is 3/27 = 1/9 tadaaaa!
got it 1/9 (that's writing it the hard way) 3/27 thanks for the fun
[3^(-1) /3^(-2)] = {3^[-1 - (-2)]} = 3^(-1 + 2) = 3^1 = 3 top solved that leaves us with 3/(3 * 3^2) 3's cancel leaving us with 1/(3^2) = 1/9
Subtracting the exponents I find easier than your explanation.
I solved this in my head in 1/9 of a minute.
Yes,d is the right answer i e 1/9.Thanks
Another small victory to start my day. ;)
d)
Deu 1/9, letra D.
Got it in a few seconds BUT I'm cheating. Like you I taught maths for 38 years then taught Electronic Maths at a College.
Nice review of negative exponents, but not how I would solve this. For the numerator, given the common base, divide by subtracting the exponents. -1 - -2 is one, so the numerator is 3^1 or just 3.
The denominator also has common bases, so add the exponents to multiply. 1 plus 2 is 3, so the denominator is 3^3.
Now, divide 3^1 by 3^3 by subtracting exponents, 1 minus 3, yielding 3^-2. That eliminates the fraction.
Finally, apply the inverse rule if you want, changing 3^-2 to 1/3^2 or 1/9. If 3^-2 were in the choices, that seems like it would be a valid answer.
Easy enough paper and pencil isn't required.
Here's another fun mechanism. A number to a negative power is the inverse of the number to the positive power, but that's a limited view.
The general rule is a number to any power, positive or negative (even the zero power, if minus zero doesn't bother you) equals one over the same number to the opposite sign power.
3^5 = 1/3^-5 just like 3^-5=1/3^5.
d) 1/9
1/9
Quick and easy. N. P.
A) 9
D 1/9
This problem is not that hard, but I can clearly see where common mistakes are going to be made 1/9
D
I got it without the 1/3 step. Don't get all the extra fractions.
d
Got it again🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉
1/9 is correct ans.
27
The answer is 1/9.
9
The answer is 1/9
9÷27 =1/9
Keep it short, to many examples a get confusing and loose interest, I realize one has to promote oneself. To much information all at once can be overwhelming, most people have a short attention span.
Marcus did ot take you 18 minutes
Everyone should simply ignore this mishmash of operators. Whoever wrote it lacks all sense of rigor, precision and sense.
d (awful @ math but enjoy it anyway - may be choice a, lol)
You are taking way to long to get to the answer.
B
I think it may be D?
1/9
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1/9