# How do you simplify 64^(3/4)times81^(2/3)?

May 23, 2017

$144 \cdot {2}^{\frac{1}{2}} \cdot {3}^{\frac{2}{3}}$

#### Explanation:

Step 1. Find the factors of 64 and 81
$64 = {2}^{6}$
$81 = {3}^{4}$

${64}^{\frac{3}{4}} \times {81}^{\frac{2}{3}} = {\left({2}^{6}\right)}^{\frac{3}{4}} \times {\left({3}^{4}\right)}^{\frac{2}{3}}$

Step 2. Rewrite the base numbers with powers that will reduce with the fractional exponents

${\left({2}^{2} \cdot {2}^{4}\right)}^{\frac{3}{4}} \times {\left({3}^{1} \cdot {3}^{3}\right)}^{\frac{2}{3}}$

Step 3. Multiply the fractional powers through

$\left({2}^{\frac{3}{2}} \cdot {2}^{3}\right) \times \left({3}^{\frac{2}{3}} \cdot {3}^{2}\right)$

$\left({\left(2 \cdot {2}^{2}\right)}^{\frac{1}{2}} \cdot {2}^{3}\right) \times \left({3}^{\frac{2}{3}} \cdot {3}^{2}\right)$

$\left({2}^{\frac{1}{2}} \cdot 2 \cdot {2}^{3}\right) \times \left({3}^{\frac{2}{3}} \cdot {3}^{2}\right)$

$144 \cdot {2}^{\frac{1}{2}} \cdot {3}^{\frac{2}{3}}$