# How do you simplify 8^(2/3) * 8?

Oct 30, 2015

Ans: ${8}^{\frac{5}{3}}$ or $\sqrt{{8}^{5}}$ or $32$

#### Explanation:

${8}^{\frac{2}{3}}$ can be written as $\sqrt{{8}^{2}}$.

If you know that ${8}^{2}$ is $64$, and that cube root of $64$ (root(3)64) is $4$, then this it is easy to solve the problem in this way.

You could also write ${8}^{\frac{2}{3}}$ as $\sqrt{8 \cdot 8}$.

Take the cube root of each $8$ separately and multiply them

${8}^{\frac{2}{3}} \cdot 8$

($\sqrt{8} \cdot \sqrt{8}$)*8

$\left(2 \cdot 2\right) \cdot 8$

$4 \cdot 8$

$32$

Another way to solve this:

When two numbers are being multiplied (${8}^{\frac{2}{3}}$ and $8$) and their bases ($8$) are the same, the product can simply be written as the base ($8$) to the power of the addition of the powers ($\frac{2}{3} + 1$)

${8}^{\frac{2}{3}} \cdot {8}^{1}$

${8}^{\frac{2}{3} + 1}$

${8}^{\frac{5}{3}}$

${8}^{\frac{5}{3}}$ can be written as $\sqrt{{8}^{5}}$

$\sqrt{{8}^{5}}$

$\sqrt{8 \cdot 8 \cdot 8 \cdot 8 \cdot 8}$

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$

$32$