Algebra Examples

${(16^{3})}^{\frac{1}{2}}$

Step 1

Multiply the exponents in ${(16^{3})}^{\frac{1}{2}}$ .

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Step 1.1

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

$16^{3 (\frac{1}{2})}$

Step 1.2

Combine $3$ and $\frac{1}{2}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$4^{3}$

Step 5

Raise $4$ to the power of $3$ .

$64$