Simplify 7 square root of 2* square root of 5* square root of 10

$7 \sqrt{2} \cdot \sqrt{5} \cdot \sqrt{10}$

Multiply $7 \sqrt{2} \sqrt{5}$ .

Combine using the product rule for radicals.

$7 \sqrt{5 \cdot 2} \cdot \sqrt{10}$

Multiply $5$ by $2$ .

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

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

Raise $\sqrt{10}$ to the power of $1$ .

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

Raise $\sqrt{10}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$7 \cdot 10^{1}$

Evaluate the exponent.

$7 \cdot 10$

Multiply $7$ by $10$ .

$70$