Algebra Examples

$\frac{2^{\frac{2}{3}} \cdot 16^{\frac{2}{3}}}{4^{\frac{2}{3}}}$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $4$ by $2$ .

$\frac{2^{\frac{2}{3}} \cdot 2^{\frac{8}{3}}}{4^{\frac{2}{3}}}$

Step 3

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

$\frac{2^{\frac{2}{3} + \frac{8}{3}}}{4^{\frac{2}{3}}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2^{\frac{2 + 8}{3}}}{4^{\frac{2}{3}}}$

Step 5

Add $2$ and $8$ .

$\frac{2^{\frac{10}{3}}}{4^{\frac{2}{3}}}$