Write the function without radicals by using fractional exponents.
-$$y = \sqrt [ 3 ] { ( 2 x ) ^ { 2 } } + \sqrt { ( 8 x ) ^ { 3 } }$$
A) $y = ( 2 x ) ^ { 2 / 3 } + ( 8 x ) ^ { 3 }$
B) $y = ( 2 x ) ^ { 3 / 2 } + ( 8 x ) ^ { 2 / 3 }$
C) $y = ( 10 x ) ^ { 13 / 6 }$
D) $y = ( 2 x ) ^ { 2 / 3 } + ( 8 x ) ^ { 3 / 2 }$

Question

Quizplus · Accepted Answer

The conversion from a radical to a fractional exponent involves using the rule $\sqrt[n]{x^m} = x^{m/n}$. For the first term, $\sqrt[3]{(2x)^2}$ becomes $(2x)^{2/3}$. For the second term, $\sqrt{(8x)^3}$ is equivalent to $(8x)^{3/2}$, making option D correct.

Write the Function Without Radicals by Using Fractional Exponents y=(2x)23+(8x)3y = \sqrt [ 3 ] { ( 2 x ) ^ { 2 } } + \sqrt { ( 8 x ) ^ { 3 } }y=3(2x)2​+(8x)3​

Write the Function Without Radicals by Using Fractional Exponents $y = \sqrt [ 3 ] { ( 2 x ) ^ { 2 } } + \sqrt { ( 8 x ) ^ { 3 } }$