Mathematics: Simplify the expression. (-1)^5^2/(-2)^-3^2 a) 64 b) 2^-30 c) 2^30 d) 1/64

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Simplify the expression. (-1)^5^2/(-2)^-3^2 a) 64

andybiersack154

15.01.2022

Option A is correct.

A) 64

Step-by-step explanation:

Given:

The given expression = $\frac{(-1^5)^2}{(-2^{-3})^2}$

Now we need to simplify the given expression.

Solution:

= $\frac{(-1^5)^2}{(-2^{-3})^2}$

Rewrite the expression as.

= $(\frac{(-1)^5}{(-2)^{-3}})^{2}$ -------(1)

First we expand numerator $(-1)^{5}=(-1\times -1)\times (-1\times -1)\times -1$

$=(1)\times (1)\times -1$

$=(1\times 1)\times -1$

$=1\times -1$

$(-1)^{5}= -1$

Similarly we simplify the denominator $(-2)^{-3}$ .

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

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

$(-2)^{-3}=\frac{1}{4\times -2}$

$(-2)^{-3}=\frac{1}{-8}$

Now we substitute $(-1)^{5}=-1$ and $(-2)^{-3}=\frac{1}{-8}$ in equation 1.

$(\frac{(-1)^5}{(-2)^{-3}})^{2}=(\frac{-1}{\frac{1}{-8}})^{2}$

Negative sign is cancelled.

$(\frac{(-1)^5}{(-2)^{-3}})^{2}=(\frac{1}{\frac{1}{8}})^{2}$

So we write the equation as.

$(\frac{(-1)^5}{(-2)^{-3}})^{2}=8^{2}$

$(\frac{(-1)^5}{(-2)^{-3}})^{2}= 64$

Therefore the answer is 64

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