Evaluate 64^(2/3)*64^(2/3)

$64^{\frac{2}{3}} \cdot 64^{\frac{2}{3}}$

Step 1

Multiply $64^{\frac{2}{3}}$ by $64^{\frac{2}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$64^{\frac{2}{3} + \frac{2}{3}}$

Combine the numerators over the common denominator.

$64^{\frac{2 + 2}{3}}$

Add $2$ and $2$ .

$64^{\frac{4}{3}}$

Step 2

Simplify the expression.

Rewrite $64$ as $4^{3}$ .

${(4^{3})}^{\frac{4}{3}}$

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

$4^{3 (\frac{4}{3})}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$4^{3 (\frac{4}{3})}$

Rewrite the expression.

$4^{4}$

Step 4

Raise $4$ to the power of $4$ .

$256$