Question

simplify [3^-1/(-2)^-2]^-2​

Answer 1

31=3

Explanation:

Rules of exponents says

(am)n=amn

Where

a=3

m=12

n=2

So

(312)2=3(12)⋅2

(312)2=31

31=3

Answer 2

Answer: $\frac{9}{16}$

Step-by-step explanation:

$(\frac{3^{-1}}{(-2)^{-2}})^{-2}$

First according to BODMAS, you have to solve the brackets.

If power is given in negative value then you have to change it into reciprocal. (upside down) and write as positive index.

$(\frac{(-2)^{2}}{3^{1}})^{-2}$

*If the index is an even number and the base is in negative, then the answer will be positive.

*If the index is an odd number and the base is in negative, then the answer will be negative.

Here for -2 index is even. So answer will be positive.

$(\frac{4}{3}) ^{-2}$

If power is given in negative value then you have to change it into reciprocal. (upside down) and write as positive index.

$(\frac{3}{4}) ^{2}$

=$\frac{9}{16}$

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