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

Question

asked Apr 5, 2022 38.7k views

1 Answer

Strange Quark · Answer 1 · 2022-04-09T08:22:52+0000

Answer:

(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