Simplify (27*64)^(2/3)

${(27 \cdot 64)}^{\frac{2}{3}}$

Step 1

Simplify the expression.

Multiply $27$ by $64$ .

$1728^{\frac{2}{3}}$

Rewrite $1728$ as $12^{3}$ .

${(12^{3})}^{\frac{2}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$12^{3 (\frac{2}{3})}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$12^{3 (\frac{2}{3})}$

Rewrite the expression.

$12^{2}$

Step 3

Raise $12$ to the power of $2$ .

$144$