Question

Which expression is equivalent to (125^2 / 125^4/3)
algebra II engenuity

Answer 1

Answer: Last option.

Explanation:

To find which expression in equivalent to the expression
`(125^2)/(125^(4)/(3) )`, you need to remember :

The Power of a power property:

`(a^m)^n=a^((mn))`

The Quotient of powers property:

`(a^m)/(a^n) =a^((m-n))`

And the Product of powers property:

`(a^m)(a^n)=a^((m+n))`

Knowing that:

`125=5*5*5=5^3`

Then, you get:

`(125^2)/(125^(4)/(3) )=((5^3)^2)/((5^3)^(4)/(3) )=(5^6)/(5^4)=5^((6-4))=5^2=25`