Simplify square root of (4r^8)/(t^9)

$\sqrt{\frac{4 r^{8}}{t^{9}}}$

Rewrite $\frac{4 r^{8}}{t^{9}}$ as ${(\frac{2 r^{4}}{t^{4}})}^{2} \frac{1}{t}$ .

Factor the perfect power ${(2 r^{4})}^{2}$ out of $4 r^{8}$ .

$\sqrt{\frac{{(2 r^{4})}^{2} \cdot 1}{t^{9}}}$

Factor the perfect power ${(t^{4})}^{2}$ out of $t^{9}$ .

$\sqrt{\frac{{(2 r^{4})}^{2} \cdot 1}{{(t^{4})}^{2} t}}$

Rearrange the fraction $\frac{{(2 r^{4})}^{2} \cdot 1}{{(t^{4})}^{2} t}$ .

$\sqrt{{(\frac{2 r^{4}}{t^{4}})}^{2} \frac{1}{t}}$

Pull terms out from under the radical.

$\frac{2 r^{4}}{t^{4}} \sqrt{\frac{1}{t}}$

Rewrite $\sqrt{\frac{1}{t}}$ as $\frac{\sqrt{1}}{\sqrt{t}}$ .

$\frac{2 r^{4}}{t^{4}} \cdot \frac{\sqrt{1}}{\sqrt{t}}$

Combine.

$\frac{2 r^{4} \sqrt{1}}{t^{4} \sqrt{t}}$

Simplify the numerator.

Any root of $1$ is $1$ .

$\frac{2 r^{4} \cdot 1}{t^{4} \sqrt{t}}$

Multiply $2$ by $1$ .

$\frac{2 r^{4}}{t^{4} \sqrt{t}}$

Multiply $\frac{2 r^{4}}{t^{4} \sqrt{t}}$ by $\frac{\sqrt{t}}{\sqrt{t}}$ .

$\frac{2 r^{4}}{t^{4} \sqrt{t}} \cdot \frac{\sqrt{t}}{\sqrt{t}}$

Combine and simplify the denominator.

Multiply $\frac{2 r^{4}}{t^{4} \sqrt{t}}$ by $\frac{\sqrt{t}}{\sqrt{t}}$ .

$\frac{2 r^{4} \sqrt{t}}{t^{4} \sqrt{t} \sqrt{t}}$

Move $\sqrt{t}$ .

$\frac{2 r^{4} \sqrt{t}}{t^{4} (\sqrt{t} \sqrt{t})}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} ({\sqrt{t}}^{1} \sqrt{t})}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} ({\sqrt{t}}^{1} {\sqrt{t}}^{1})}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} {\sqrt{t}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 r^{4} \sqrt{t}}{t^{4} {\sqrt{t}}^{2}}$

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

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} {(t^{\frac{1}{2}})}^{2}}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} t^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} t^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 r^{4} \sqrt{t}}{t^{4} t^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 r^{4} \sqrt{t}}{t^{4} t^{1}}$

Simplify.

$\frac{2 r^{4} \sqrt{t}}{t^{4} t}$

Multiply $t^{4}$ by $t$ by adding the exponents.

Multiply $t^{4}$ by $t$ .

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

$\frac{2 r^{4} \sqrt{t}}{t^{4} t^{1}}$

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

$\frac{2 r^{4} \sqrt{t}}{t^{4 + 1}}$

Add $4$ and $1$ .

$\frac{2 r^{4} \sqrt{t}}{t^{5}}$

Simplify square root of (4r^8)/(t^9)

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