Use rational exponents to simplify. Write the answer in radical notation if appropriate.
-$\frac { \sqrt [ 5 ] { x ^ { 5 } } } { \sqrt [ 5 ] { x ^ { 7 } } }$
A) $\frac { 1 } { x ^ { 2 } }$
B) $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$
C) $\sqrt [ 5 ] { \mathrm { x } ^ { 2 } }$
D) $\sqrt [ 7 ] { \mathrm { x } ^ { 12 } }$

Question

Quizplus · Accepted Answer

The expression simplifies to $\frac { 1 } { \sqrt [ 5 ] { x ^ { 2 } } }$ by subtracting the exponents in the denominator from the numerator under the same root, resulting in $x^{(5-7)/5} = x^{-2/5}$, which is option B.

Use Rational Exponents to Simplify x55x75\frac { \sqrt [ 5 ] { x ^ { 5 } } } { \sqrt [ 5 ] { x ^ { 7 } } }5x7​5x5​​

Use Rational Exponents to Simplify $\frac { \sqrt [ 5 ] { x ^ { 5 } } } { \sqrt [ 5 ] { x ^ { 7 } } }$