Solve =(8x)^2/3+(8x)^-2/3

$$= ( 8 x ) ^ { 2 / 3 } + ( 8 x ) ^ { - 2 / 3 }$$

Evaluate

$$4x^{\frac{2}{3}}+\frac{1}{4x^{\frac{2}{3}}}$$

Solution Steps

Expand \left(8x\right)^{\frac{2}{3}}.

$$8^{\frac{2}{3}}x^{\frac{2}{3}}+\left(8x\right)^{-\frac{2}{3}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$4x^{\frac{2}{3}}+\left(8x\right)^{-\frac{2}{3}}$$

Expand \left(8x\right)^{-\frac{2}{3}}.

$$4x^{\frac{2}{3}}+8^{-\frac{2}{3}}x^{-\frac{2}{3}}$$

Calculate 8 to the power of -\frac{2}{3} and get \frac{1}{4}.

$$4x^{\frac{2}{3}}+\frac{1}{4}x^{-\frac{2}{3}}$$

Factor

$$\frac{16x^{\frac{4}{3}}+1}{4x^{\frac{2}{3}}}$$