Question

Determine whether

Answer 1

Answer:

(a) and (b) are not equivalent

(c) is equivalent

Step-by-step explanation:

Given

$\frac{25^m}{5}$

Required

Determine an equivalent or nonequivalent expression

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

We have:

$25^{m-1$

Apply law of indices

$25^{m-1} = \frac{25^m}{25}$

This is not equivalent to $\frac{25^m}{5}$

$(b)\ 25^{2m - 1}$

We have:

$25^{2m - 1}$

Apply law of indices

$25^{2m - 1} = \frac{25^{2m}}{25}$

This is not equivalent to $\frac{25^m}{5}$

$(c)\ 5^{2m-1}$

We have:

$5^{2m-1}$

Apply law of indices

$5^{2m-1} = \frac{5^{2m}}{5^1}$

$5^{2m-1} = \frac{5^{2m}}{5}$

Evaluate the numerator

$5^{2m-1} = \frac{25m}{5}$

This is an equivalent expression