Question

Show all work to write the expression in simplified radical form:
$(8x)^{\frac{2}{3}}$
(Eight x to the two thirds power)

Answer 1

Answer:0.08333333....

Step-by-step explanation:

Answer 2

Answer:

4x²

Step-by-step explanation:

Normally you would use the exponent → roots rule, but this one simplifies easier without that

$(8x)^{\frac{2}{3} }$

8 = 2³

so $(8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}}$

then the threes cancel, since one is a 3 and the other one is $\frac{1}{3}$

so $(8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2$

then just square the 2 and the x

$(8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2 = 4x^2$