Question

Which expressions are equivalent to the one below? Check all that apply.

Answer 1

Use two main properties for powers:

1. $(a^m)^n=a^{m\cdot n};$

2. $\dfrac{a^m}{a^n}=a^{m-n}.$

The expression $\dfrac{25^x}{5^x}$ can be simplified in following way:

$\dfrac{25^x}{5^x}=\dfrac{(5^2)^x}{5^x}=\dfrac{5^{2x}}{5^x}=5^{2x-x}=5^x.$

Then the expression $\dfrac{25^x}{5^x}$ is equivalent to $5^x.$

Answer: correct choice is D

Answer 2

The answer is E:5
a^n/b^m=a/b^n/m
So x/x=1 and 25/5=5
Then 5^1=5