Question

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

5^3•5^x
A. 5^3x
B. 5^3+x
C. 25^3x
D. 125•5^x
E. (5•x) ³
F. 5^3-x

Answer 1

B.
`5^3+x`

D.
`125.5^x`

Explanation:

Given expression is,

`5^3.5^x`

`=125.5^x`

In option A,

`5^(3x)=(5^3)^x=125^x` (
`(a^m)^n=a^(mn)` )

In option B,

`5^(3+x)=5^3.5^x=125.5^x` (
`a^(m+n)=a^m.a^n` )

In option C,

`25^3x=15625x`

In option D,

`125.5^x`

In option E,

`(5x)^3=5^3.x^3=125x^3` (
`(ab)^m=a^m.b^m` )

In option F,

`5^(3-x)=(5^3)/(5^x)=(125)/(5^x)` (
`a^(m-n)=(a^m)/(a^n)` )

Hence, by the above explanation it is clear that option B and option D are equivalent to the given expression.