Write $x ^ { \frac { 2 } { 7 } }$ in radical form.
A) $\sqrt [ 7 ] { x ^ { 2 } }$
B) $\sqrt [ 7 ] { x ^ { 7 } }$
C) $\sqrt { x }$
D) $\sqrt [ 7 ] { x }$

Question

Write  $x ^ { \frac { 2 } { 7 } }$  in radical form.
A) $\sqrt [ 7 ] { x ^ { 2 } }$
B) $\sqrt [ 7 ] { x ^ { 7 } }$
C) $\sqrt { x }$
D) $\sqrt [ 7 ] { x }$

Quizplus · Accepted Answer

To convert $x ^ {\frac{2}{7}}$ to radical form, we need the exponent to be in the form of $\frac{1}{n}$. In this case, we can rewrite $\frac{2}{7}$ as $\frac{1}{7}+\frac{1}{7}$. Then, using the rule $a^{m+n}=a^m\cdot a^n$, we have:

$$x ^ {\frac { 2 } { 7 } }=x^{\frac{1}{7}+\frac{1}{7}}=\sqrt [ 7 ] { x ^ { 1 } }\cdot \sqrt [ 7 ] { x ^ { 1 } }=\sqrt [ 7 ] { x ^ { 2 } }$$

Therefore, the best choice is A.

Write x27x ^ { \frac { 2 } { 7 } }x72​

Write $x ^ { \frac { 2 } { 7 } }$