Solve for c c=72(27)^(2/3)

$c = 72 {(27)}^{\frac{2}{3}}$

Step 1

Remove parentheses.

$c = 72 \cdot 27^{\frac{2}{3}}$

Step 2

Simplify $72 \cdot 27^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $27$ as $3^{3}$ .

$c = 72 \cdot {(3^{3})}^{\frac{2}{3}}$

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

$c = 72 \cdot 3^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$c = 72 \cdot 3^{3 (\frac{2}{3})}$

Rewrite the expression.

$c = 72 \cdot 3^{2}$

Simplify the expression.

Raise $3$ to the power of $2$ .

$c = 72 \cdot 9$

Multiply $72$ by $9$ .

$c = 648$