Algebra Examples

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

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

$16^{\frac{3}{2} \cdot \frac{1}{2}}$

Step 1.1.2

Multiply $\frac{3}{2} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 1.1.2.1

Multiply $\frac{3}{2}$ by $\frac{1}{2}$ .

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

Step 1.1.2.2

Multiply $2$ by $2$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$2^{3}$

Step 3

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

$8$