Write in radical form. Assume all variables represent positive real numbers.
-$$( 3 m + 3 n ) ^ { 3 / 5 }$$
A) $\sqrt [ 5 ] { 3 m + 3 n ^ { 3 } }$

B) $\sqrt [ 3 ] { 3 m + 3 n ^ { 5 } }$

C) $\sqrt [ 5 ] { ( 3 m + 3 n ) ^ { 3 } }$

D) $\sqrt [ 3 ] { ( 3 m + 3 n ) ^ { 5 } }$

Question

Write in radical form. Assume all variables represent positive real numbers.
-$$( 3 m + 3 n ) ^ { 3 / 5 }$$
A) $\sqrt [ 5 ] { 3 m + 3 n ^ { 3 } }$

B) $\sqrt [ 3 ] { 3 m + 3 n ^ { 5 } }$

C) $\sqrt [ 5 ] { ( 3 m + 3 n ) ^ { 3 } }$

D) $\sqrt [ 3 ] { ( 3 m + 3 n ) ^ { 5 } }$

Quizplus · Accepted Answer

The correct radical form of $( 3 m + 3 n ) ^ { 3 / 5 }$ is $\sqrt [ 5 ] { ( 3 m + 3 n ) ^ { 3 } }$, which matches choice C. This is because the exponent $3/5$ can be interpreted as raising the quantity $(3m + 3n)$ to the third power and then taking the fifth root of the result.

Write in Radical Form (3m+3n)3/5( 3 m + 3 n ) ^ { 3 / 5 }(3m+3n)3/5

Write in Radical Form $( 3 m + 3 n ) ^ { 3 / 5 }$