Question

Which of the following expressions are equivalent to 4^-3/4^-8?

Answer 1

A&D

1 & 4

`(4^8)/(4^3)` and
`4^(5)`

Explanation:

edge 2021

Answer 2

A.
`(4^(8) )/(4^3)`

D.
`4^(5)`

Explanation:

We have to calculate to find the result -

The expression is = 4^(-3)/4^(-8)

According to the indices rule, the power will be deducted if it is a division.

Therefore,
`(a^(m) )/(a^(n) )` =
`a^(m-n)`

Using that formula,

=
`4^(-3-(-8))`

=
`4^(-3+8)`

=
`4^(5)`

Therefore, the answer choice D is the option, and the answer is 4^5.

Option A is also correct. Because we can find 4^5 with the help of that option.

`(4^8)/(4^3)`

=
`4^(5)`

Alternative way,

4^(-3)/4^(-8)

= 4^(-3+8)

= 4^(8-3)

= 4^8/4^3

In the is way, we can also find option A is correct.