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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

1 Answer

1 vote

Answer:

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.

User Masud Jahan
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