Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 8 / 3 } }$$
A) $\frac { 1 } { x ^ { 26 / 3 } }$
B) $x^{ 26 / 3}$
C) $x ^ { 22 / 3 }$
D) $\frac { 1 } { x ^ { 22 / 3 } }$

Question

Quizplus · Accepted Answer

To simplify the given expression, apply the rules of exponents: $\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 8 / 3 } }$ simplifies to $\frac { x ^ { 2 / 3 } } { x ^ { 8 } }$. When dividing powers with the same base, subtract the exponents: $x^{(2/3) - 8} = x^{(2/3) - (24/3)} = x^{-22/3}$. Therefore, the answer is $\frac { 1 } { x ^ { 22 / 3 } }$.

Perform the Indicated Operations (x1/3)2(x3)8/3\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 8 / 3 } }(x3)8/3(x1/3)2​

Perform the Indicated Operations $\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 8 / 3 } }$