Answer:
Option A is correct.
A) 64
Step-by-step explanation:
Given:
The given expression = [tex]\frac{(-1^5)^2}{(-2^{-3})^2}[/tex]
Now we need to simplify the given expression.
Solution:
= [tex]\frac{(-1^5)^2}{(-2^{-3})^2}[/tex]
Rewrite the expression as.
= [tex](\frac{(-1)^5}{(-2)^{-3}})^{2}[/tex]-------(1)
First we expand numerator [tex](-1)^{5}=(-1\times -1)\times (-1\times -1)\times -1[/tex]
[tex]=(1)\times (1)\times -1[/tex]
[tex]=(1\times 1)\times -1[/tex]
[tex]=1\times -1[/tex]
[tex](-1)^{5}= -1[/tex]
Similarly we simplify the denominator [tex](-2)^{-3}[/tex].
[tex](-2)^{-3}=\frac{1}{(-2)^{3}}[/tex]
[tex](-2)^{-3}=\frac{1}{(-2\times -2)\times -2}[/tex]
[tex](-2)^{-3}=\frac{1}{4\times -2}[/tex]
[tex](-2)^{-3}=\frac{1}{-8}[/tex]
Now we substitute [tex](-1)^{5}=-1[/tex] and [tex](-2)^{-3}=\frac{1}{-8}[/tex] in equation 1.
[tex](\frac{(-1)^5}{(-2)^{-3}})^{2}=(\frac{-1}{\frac{1}{-8}})^{2}[/tex]
Negative sign is cancelled.
[tex](\frac{(-1)^5}{(-2)^{-3}})^{2}=(\frac{1}{\frac{1}{8}})^{2}[/tex]
So we write the equation as.
[tex](\frac{(-1)^5}{(-2)^{-3}})^{2}=8^{2}[/tex]
[tex](\frac{(-1)^5}{(-2)^{-3}})^{2}= 64[/tex]
Therefore the answer is 64
