Question
Simplify $:\left(8 x^3 \div 125 y^3\right)^{\frac{2}{3}}$
✓
Answer
$ \left(8 x^3 \div 125 y^3\right)^{\frac{2}{3}}$
$ =\left(\frac{2 x \times 2 x \times 2 x}{5 y \times 5 y \times 5 y}\right)^{\frac{2}{3}}$
$ =\left[\left(\frac{2 x}{5 y}\right)^3\right]^{\frac{2}{3}}$
$ =\left(\frac{2 x}{5 y}\right)^{3 \times \frac{2}{3}}$
$ =\left(\frac{2 x}{5 y}\right)^2$
$ =\left[\frac{2 x}{5 y} \times \frac{2 x}{5 y}\right]$
$ =\frac{4 x^2}{25 y^2}$
$ =\left(\frac{2 x \times 2 x \times 2 x}{5 y \times 5 y \times 5 y}\right)^{\frac{2}{3}}$
$ =\left[\left(\frac{2 x}{5 y}\right)^3\right]^{\frac{2}{3}}$
$ =\left(\frac{2 x}{5 y}\right)^{3 \times \frac{2}{3}}$
$ =\left(\frac{2 x}{5 y}\right)^2$
$ =\left[\frac{2 x}{5 y} \times \frac{2 x}{5 y}\right]$
$ =\frac{4 x^2}{25 y^2}$
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