Question

Will fan and medal whoever checks my work.
3 ^-2
( ----- )
5y^4

A.
6
-----
10y^16
B.
10y^16
-----
6
C.
9
-----
25y^8
D.
25y^8
-----
9
I think it is C.

Answer 1

wrong notice the exponent have a negative sign

Answer 2

\[\large\rm a^{-1}= \frac{1}{a}\]

Answer 3

first solve the problem as if there was no negative sign. After that just make its reciprocal.

Answer 4

I still don't get it. I understood the first one because it didn't have a negative. Negatives get me SO confused.

Answer 5

Okay should I walk you through the solution?

Answer 6

I think that would help yeah lol

Answer 7

\[\large\rm \frac{3}{5y^4}^{-2}\]\[\large\rm 3^{-2}*\frac{1}{5y^4}^{-2}\]\[\large\rm 9^{-1}*\frac{1}{25y^8}^{-1}\]
So far everything clear?

Answer 8

Yes

Answer 9

\[\large\rm a^{-1}=\frac{1}{a}\]\[\large\rm \frac{1}{a}^{-1}=a\]
Agree?

Answer 10

Yes

Answer 11

\[\large\rm 9^{-1}=\frac{1}{9} \] \[\large\rm \frac{1}{25y^8}^{-1}=25y^8\] Can you work out the answer now

Answer 12

So it's D?

Answer 13

yes, it's D.

The fast way is if you see a negative exponent, "flip" the fraction, and at the same time make the exponent positive

so when you see
\[ \left(\frac{3}{5y^4}\right)^{-2} \]
flip the fraction and make the -2 a +2
\[ \left(\frac{5y^4}{3}\right)^{2} \]
now do the normal thing

Answer 14

Yep it is D