Rewrite the expression using rational exponents. $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$
A) $\frac { 1 } { x ^ { 2 / 3 } }$
B) $x ^ { 3 }$
C) $\frac { 1 } { x ^ { 2 } }$
D) $\frac { 1 } { x ^ { 3 } }$
E) $x ^ { 2 }$

Question

Quizplus · Accepted Answer

Using the quotient property of radicals, we can simplify the expression to:
$$\frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}=\sqrt[3]{\frac{x^5}{x^7}}=\sqrt[3]{\frac{1}{x^2}}=\frac{1}{\sqrt[3]{x^2}}=\frac{1}{x^{2/3}}$$ Therefore, the answer is choice A.

Rewrite the Expression Using Rational Exponents x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }3x7​3x5​​

Rewrite the Expression Using Rational Exponents $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$