Simplify 1/5 square root of 5n^3* square root of 20n^5

$\frac{1}{5} \sqrt{5 n^{3}} \cdot \sqrt{20 n^{5}}$

Rewrite $5 n^{3}$ as $n^{2} \cdot (5 n)$ .

Factor out $n^{2}$ .

$\frac{1}{5} \cdot \sqrt{5 (n^{2} n)} \cdot \sqrt{20 n^{5}}$

Reorder $5$ and $n^{2}$ .

$\frac{1}{5} \cdot \sqrt{n^{2} \cdot 5 n} \cdot \sqrt{20 n^{5}}$

Add parentheses.

$\frac{1}{5} \cdot \sqrt{n^{2} \cdot (5 n)} \cdot \sqrt{20 n^{5}}$

Pull terms out from under the radical.

$\frac{1}{5} \cdot (n \sqrt{5 n}) \cdot \sqrt{20 n^{5}}$

Multiply $\frac{1}{5} (n \sqrt{5 n})$ .

Combine $n$ and $\frac{1}{5}$ .

$\frac{n}{5} \sqrt{5 n} \cdot \sqrt{20 n^{5}}$

Combine $\frac{n}{5}$ and $\sqrt{5 n}$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{20 n^{5}}$

Rewrite $20 n^{5}$ as ${(2 n^{2})}^{2} \cdot (5 n)$ .

Factor $4$ out of $20$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{4 (5) n^{5}}$

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

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{2^{2} \cdot 5 n^{5}}$

Factor out $n^{4}$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{2^{2} \cdot 5 (n^{4} n)}$

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{2^{2} \cdot 5 ({(n^{2})}^{2} n)}$

Move $5$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{2^{2} {(n^{2})}^{2} \cdot 5 n}$

Rewrite $2^{2} {(n^{2})}^{2}$ as ${(2 n^{2})}^{2}$ .

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{{(2 n^{2})}^{2} \cdot 5 n}$

Add parentheses.

$\frac{n \sqrt{5 n}}{5} \cdot \sqrt{{(2 n^{2})}^{2} \cdot (5 n)}$

Pull terms out from under the radical.

$\frac{n \sqrt{5 n}}{5} \cdot (2 n^{2} \sqrt{5 n})$

Rewrite using the commutative property of multiplication.

$2 \frac{n \sqrt{5 n}}{5} (n^{2} \sqrt{5 n})$

Combine $2$ and $\frac{n \sqrt{5 n}}{5}$ .

$\frac{2 (n \sqrt{5 n})}{5} (n^{2} \sqrt{5 n})$

Multiply $\frac{2 n \sqrt{5 n}}{5} (n^{2} \sqrt{5 n})$ .

Combine $n^{2}$ and $\frac{2 n \sqrt{5 n}}{5}$ .

$\frac{n^{2} (2 n \sqrt{5 n})}{5} \sqrt{5 n}$

Multiply $n^{2}$ by $n$ by adding the exponents.

Move $n$ .

$\frac{n \cdot n^{2} (2 \sqrt{5 n})}{5} \sqrt{5 n}$

Multiply $n$ by $n^{2}$ .

Raise $n$ to the power of $1$ .

$\frac{n^{1} n^{2} (2 \sqrt{5 n})}{5} \sqrt{5 n}$

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

$\frac{n^{1 + 2} (2 \sqrt{5 n})}{5} \sqrt{5 n}$

Add $1$ and $2$ .

$\frac{n^{3} (2 \sqrt{5 n})}{5} \sqrt{5 n}$

Combine $\frac{n^{3} (2 \sqrt{5 n})}{5}$ and $\sqrt{5 n}$ .

$\frac{n^{3} (2 \sqrt{5 n}) \sqrt{5 n}}{5}$

Raise $\sqrt{5 n}$ to the power of $1$ .

$\frac{n^{3} (2 ({\sqrt{5 n}}^{1} \sqrt{5 n}))}{5}$

Raise $\sqrt{5 n}$ to the power of $1$ .

$\frac{n^{3} (2 ({\sqrt{5 n}}^{1} {\sqrt{5 n}}^{1}))}{5}$

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

$\frac{n^{3} (2 {\sqrt{5 n}}^{1 + 1})}{5}$

Add $1$ and $1$ .

$\frac{n^{3} (2 {\sqrt{5 n}}^{2})}{5}$

Simplify the numerator.

Rewrite.

$\frac{n^{3} (2 \sqrt{5 n}) \sqrt{5 n}}{5}$

Raise $\sqrt{5 n}$ to the power of $1$ .

$\frac{n^{3} (2 ({\sqrt{5 n}}^{1} \sqrt{5 n}))}{5}$

Raise $\sqrt{5 n}$ to the power of $1$ .

$\frac{n^{3} (2 ({\sqrt{5 n}}^{1} {\sqrt{5 n}}^{1}))}{5}$

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

$\frac{n^{3} (2 {\sqrt{5 n}}^{1 + 1})}{5}$

Add $1$ and $1$ .

$\frac{n^{3} (2 {\sqrt{5 n}}^{2})}{5}$

Remove unnecessary parentheses.

$\frac{n^{3} \cdot 2 {\sqrt{5 n}}^{2}}{5}$

Rewrite ${\sqrt{5 n}}^{2}$ as $5 n$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 n}$ as ${(5 n)}^{\frac{1}{2}}$ .

$\frac{n^{3} \cdot 2 {({(5 n)}^{\frac{1}{2}})}^{2}}{5}$

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

$\frac{n^{3} \cdot 2 {(5 n)}^{\frac{1}{2} \cdot 2}}{5}$

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

$\frac{n^{3} \cdot 2 {(5 n)}^{\frac{2}{2}}}{5}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{n^{3} \cdot 2 {(5 n)}^{\frac{2}{2}}}{5}$

Rewrite the expression.

$\frac{n^{3} \cdot 2 {(5 n)}^{1}}{5}$

Simplify.

$\frac{n^{3} \cdot 2 (5 n)}{5}$

$\frac{n^{3} \cdot 2 \cdot 5 n}{5}$

Combine exponents.

Multiply $5$ by $2$ .

$\frac{n^{3} \cdot 10 n}{5}$

Raise $n$ to the power of $1$ .

$\frac{10 (n^{3} n^{1})}{5}$

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

$\frac{10 n^{3 + 1}}{5}$

Add $3$ and $1$ .

$\frac{10 n^{4}}{5}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 n^{4}$ .

$\frac{5 (2 n^{4})}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\frac{5 (2 n^{4})}{5 (1)}$

Cancel the common factor.

$\frac{5 (2 n^{4})}{5 \cdot 1}$

Rewrite the expression.

$\frac{2 n^{4}}{1}$

Divide $2 n^{4}$ by $1$ .

$2 n^{4}$

Simplify 1/5 square root of 5n^3* square root of 20n^5

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