Simplify the Radical Expression 5 square root of 7*2 square root of 7

$5 \sqrt{7} \cdot 2 \sqrt{7}$

Multiply $2$ by $5$ .

$10 \sqrt{7} \sqrt{7}$

Multiply $10 \sqrt{7} \sqrt{7}$ .

Raise $\sqrt{7}$ to the power of $1$ .

$10 ({\sqrt{7}}^{1} \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$10 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

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

$10 {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$10 {\sqrt{7}}^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$10 {(7^{\frac{1}{2}})}^{2}$

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

$10 \cdot 7^{\frac{1}{2} \cdot 2}$

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

$10 \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$10 \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$10 \cdot 7^{1}$

Evaluate the exponent.

$10 \cdot 7$

Multiply $10$ by $7$ .

$70$