Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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

Step 4

Multiply $\frac{2}{3} \cdot 8$ .

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Step 4.1

Combine $\frac{2}{3}$ and $8$ .

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

Step 4.2

Multiply $2$ by $8$ .

$\frac{16}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{3}$

Decimal Form:

$5.\overline{3}$

Mixed Number Form:

$5 \frac{1}{3}$