Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

Raise $4$ to the power of $1$ .

$4^{1} {(4)}^{\frac{3}{2}}$

Step 1.1.2

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

$4^{1 + \frac{3}{2}}$

Step 1.2

Write $1$ as a fraction with a common denominator.

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $2$ and $3$ .

$4^{\frac{5}{2}}$

Step 2

Simplify the expression.

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Step 2.1

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

${(2^{2})}^{\frac{5}{2}}$

Step 2.2

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

$2^{2 (\frac{5}{2})}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$2^{2 (\frac{5}{2})}$

Step 3.2

Rewrite the expression.

$2^{5}$

Step 4

Raise $2$ to the power of $5$ .

$32$