Simplify 2^(2/3)*16^(2/3)

$2^{\frac{2}{3}} \cdot 16^{\frac{2}{3}}$

Rewrite $16$ as $2^{4}$ .

$2^{\frac{2}{3}} \cdot {(2^{4})}^{\frac{2}{3}}$

Multiply the exponents in ${(2^{4})}^{\frac{2}{3}}$ .

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

$2^{\frac{2}{3}} \cdot 2^{4 (\frac{2}{3})}$

Multiply $4 (\frac{2}{3})$ .

Combine $4$ and $\frac{2}{3}$ .

$2^{\frac{2}{3}} \cdot 2^{\frac{4 \cdot 2}{3}}$

Multiply $4$ by $2$ .

$2^{\frac{2}{3}} \cdot 2^{\frac{8}{3}}$

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

$2^{\frac{2}{3} + \frac{8}{3}}$

Combine the numerators over the common denominator.

$2^{\frac{2 + 8}{3}}$

Add $2$ and $8$ .

$2^{\frac{10}{3}}$

The result can be shown in multiple forms.

Exact Form:

$2^{\frac{10}{3}}$

Decimal Form:

$10.07936839 \dots$