Question

Which expressions can be simplified as StartFraction 625 Over n Superscript 12 Baseline EndFraction? Check all that apply.

(5 n Superscript negative 3 Baseline) Superscript 4
(5 n Superscript negative 3 Baseline) Superscript negative 4
(5 n Superscript negative 4 Baseline) Superscript 3
(25 n Superscript negative 6 Baseline) Superscript negative 2
(25 n Superscript negative 6 Baseline) Superscript 2
(25 n squared) Superscript negative 6

Answer 1

The short anwser is A and E

Explanation:

Answer 2

`A. (5n^(-3))^4\\E. (25n^(-6))^(2)`

Explanation:

We are asked to determine which expressions out of the options simplifies to:

`(625)/(n^(12))=625n^(-12)`

`A. (5n^(-3))^4=5^4*n^(-3*4)=625n^(-12)\\B. (5n^(-3))^(-4)=5^(-4)*n^(-3*-4)=(1)/(625)n^(12)\\C. (5n^(-4))^3=5^3*n^(-4*3)=125n^(-12)\\\\D. (25n^(-6))^(-2)=25^(-2)*n^(-6*-2)=(1)/(625)n^(12)\\\\E. (25n^(-6))^(2)=25^(2)*n^(-6*2)=625n^(-12)\\\\F. (25n^(2))^(-6)=25^(-6)*n^(2*-6)=(1)/(25^6)n^(-12)`

From the above results, we can see that only options A and E are equivalent to the given expression.