Simplify (n^2)/( square root of 9n^11)

$\frac{n^{2}}{\sqrt{9 n^{11}}}$

Simplify the denominator.

Rewrite $9 n^{11}$ as ${(3 n^{5})}^{2} n$ .

Rewrite $9$ as $3^{2}$ .

$\frac{n^{2}}{\sqrt{3^{2} n^{11}}}$

Factor out $n^{10}$ .

$\frac{n^{2}}{\sqrt{3^{2} (n^{10} n)}}$

Rewrite $n^{10}$ as ${(n^{5})}^{2}$ .

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

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

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

Pull terms out from under the radical.

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

Cancel the common factor of $n^{2}$ and $n^{5}$ .

Multiply by $1$ .

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

Cancel the common factors.

Factor $n^{2}$ out of $3 n^{5} \sqrt{n}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3 n^{3} \sqrt{n}}$

Multiply $\frac{1}{3 n^{3} \sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{3 n^{3} \sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

$\frac{\sqrt{n}}{3 n^{3} \sqrt{n} \sqrt{n}}$

Move $\sqrt{n}$ .

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

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

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

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

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

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

$\frac{\sqrt{n}}{3 n^{3} {\sqrt{n}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

$\frac{\sqrt{n}}{3 n^{3} n^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{n}}{3 n^{3} n^{1}}$

Simplify.

$\frac{\sqrt{n}}{3 n^{3} n}$

Multiply $n^{3}$ by $n$ by adding the exponents.

Move $n$ .

$\frac{\sqrt{n}}{3 (n \cdot n^{3})}$

Multiply $n$ by $n^{3}$ .

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

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

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

$\frac{\sqrt{n}}{3 n^{1 + 3}}$

Add $1$ and $3$ .

$\frac{\sqrt{n}}{3 n^{4}}$

Simplify (n^2)/( square root of 9n^11)

Related Questions

Support LCMGCF.com by disabling your adblocker.