Question

Determine whether

25m/
5
is equivalent to each of the following expressions.
Equivalent
Not equivalent
25m-1
252m-1
52m-1

Answer 1

(a) and (b) are not equivalent

(c) is equivalent

Explanation:

Given

`(25^m)/(5)`

Required

Determine an equivalent or nonequivalent expression

`(a)\ 25^{m-1`

We have:

`25^{m-1`

Apply law of indices

`25^(m-1) = (25^m)/(25)`

This is not equivalent to
`(25^m)/(5)`

`(b)\ 25^(2m - 1)`

We have:

`25^(2m - 1)`

Apply law of indices

`25^(2m - 1) = (25^(2m))/(25)`

This is not equivalent to
`(25^m)/(5)`

`(c)\ 5^(2m-1)`

We have:

`5^(2m-1)`

Apply law of indices

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

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

Evaluate the numerator

`5^(2m-1) = (25m)/(5)`

This is an equivalent expression