Answer:
(a) and (b) are not equivalent
(c) is equivalent
Step-by-step explanation:
Given
[tex]\frac{25^m}{5}[/tex]
See attachment for complete question
Required
Determine an equivalent or nonequivalent expression
[tex](a)\ 25^{m-1[/tex]
We have:
[tex]25^{m-1[/tex]
Apply law of indices
[tex]25^{m-1} = \frac{25^m}{25}[/tex]
This is not equivalent to [tex]\frac{25^m}{5}[/tex]
[tex](b)\ 25^{2m - 1}[/tex]
We have:
[tex]25^{2m - 1}[/tex]
Apply law of indices
[tex]25^{2m - 1} = \frac{25^{2m}}{25}[/tex]
This is not equivalent to [tex]\frac{25^m}{5}[/tex]
[tex](c)\ 5^{2m-1}[/tex]
We have:
[tex]5^{2m-1}[/tex]
Apply law of indices
[tex]5^{2m-1} = \frac{5^{2m}}{5^1}[/tex]
[tex]5^{2m-1} = \frac{5^{2m}}{5}[/tex]
Evaluate the numerator
[tex]5^{2m-1} = \frac{25m}{5}[/tex]
This is an equivalent expression
