Provide an appropriate response.
-$\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$
A) $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$
B) $\sqrt [ 63 ] { z ^ { 8 } }$
C) $\sqrt [ 16 ] { \mathrm { z } ^ { 4 } }$
D) $\sqrt [ 2 ] { \mathrm { z } ^ { 4 } }$

Question

Quizplus · Accepted Answer

To simplify the given expression, $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$, we use the properties of exponents and radicals. The expression can be rewritten as $z^{4/7} / z^{4/9}$, which simplifies to $z^{(4/7)-(4/9)} = z^{(36-28)/63} = z^{8/63}$. This is equivalent to $\sqrt[63]{z^8}$, making option B correct.

Provide an Appropriate Response z47z49\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }9z4​7z4​​

Provide an Appropriate Response $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$