Question

Simplify the expression.

(-1)^5^2/(-2)^-3^2
A) 64
B) 2^-30
C) 2^30
D) 1/64

Answer 1

Option A is correct.

A) 64

Explanation:

Given:

The given expression =
`((-1^5)^2)/((-2^(-3))^2)`

Now we need to simplify the given expression.

Solution:

=
`((-1^5)^2)/((-2^(-3))^2)`

Rewrite the expression as.

=
`(((-1)^5)/((-2)^(-3)))^(2)`-------(1)

First we expand numerator
`(-1)^(5)=(-1* -1)* (-1* -1)* -1`

`=(1)* (1)* -1`

`=(1* 1)* -1`

`=1* -1`

`(-1)^(5)= -1`

Similarly we simplify the denominator
`(-2)^(-3)`.

`(-2)^(-3)=(1)/((-2)^(3))`

`(-2)^(-3)=(1)/((-2* -2)* -2)`

`(-2)^(-3)=(1)/(4* -2)`

`(-2)^(-3)=(1)/(-8)`

Now we substitute
`(-1)^(5)=-1` and
`(-2)^(-3)=(1)/(-8)` in equation 1.

`(((-1)^5)/((-2)^(-3)))^(2)=((-1)/((1)/(-8)))^(2)`

Negative sign is cancelled.

`(((-1)^5)/((-2)^(-3)))^(2)=((1)/((1)/(8)))^(2)`

So we write the equation as.

`(((-1)^5)/((-2)^(-3)))^(2)=8^(2)`

`(((-1)^5)/((-2)^(-3)))^(2)= 64`

Therefore the answer is 64