Simplify 8 square root of 2* square root of 2

$8 \sqrt{2} \cdot \sqrt{2}$

Step 1

Multiply $8 \sqrt{2} \sqrt{2}$ .

Raise $\sqrt{2}$ to the power of $1$ .

$8 ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$8 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$8 {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$8 {\sqrt{2}}^{2}$

Step 2

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$8 {(2^{\frac{1}{2}})}^{2}$

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

$8 \cdot 2^{\frac{1}{2} \cdot 2}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$8 \cdot 2^{1}$

Evaluate the exponent.

$8 \cdot 2$

Step 3

Multiply $8$ by $2$ .

$16$