# How do you simplify (64/9)^(3/2)?

Jan 28, 2018

${\left(\frac{64}{9}\right)}^{\frac{3}{2}} = \sqrt{{\left(\frac{64}{9}\right)}^{3}}$

$= \sqrt{\frac{262144}{729}}$

$= \frac{512}{27}$

Jan 28, 2018

$\frac{512}{27}$

#### Explanation:

Simplify
${\left(\frac{64}{9}\right)}^{\frac{3}{2}}$

This fractional exponent means to find the square root of the numbers raised to the third power.

sqrt(((64)/(9))^3

1) Find the square roots of the numbers
${\left(\frac{8}{3}\right)}^{3}$

2) Raise the numbers to the third power
$\frac{512}{27}$

$A n s w e r$
$\frac{512}{27}$

Here's a Khan Academy video about evaluating rational exponents: