Algebra Examples

$\frac{\sqrt{45 x^{9}}}{\sqrt{9}}$

Step 1

Combine $\sqrt{45 x^{9}}$ and $\sqrt{9}$ into a single radical.

$\sqrt{\frac{45 x^{9}}{9}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{45 x^{9}}{9}$ by cancelling the common factors.

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Step 2.1.1

Factor $9$ out of $45 x^{9}$ .

$\sqrt{\frac{9 (5 x^{9})}{9}}$

Step 2.1.2

Factor $9$ out of $9$ .

$\sqrt{\frac{9 (5 x^{9})}{9 (1)}}$

Step 2.1.3

Cancel the common factor.

$\sqrt{\frac{9 (5 x^{9})}{9 \cdot 1}}$

Step 2.1.4

Rewrite the expression.

$\sqrt{\frac{5 x^{9}}{1}}$

Step 2.2

Divide $5 x^{9}$ by $1$ .

$\sqrt{5 x^{9}}$

Step 3

Rewrite $5 x^{9}$ as ${({(x^{2})}^{2})}^{2} \cdot (5 x)$ .

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Step 3.1

Factor out $x^{8}$ .

$\sqrt{5 (x^{8} x)}$

Step 3.2

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{5 ({(x^{4})}^{2} x)}$

Step 3.3

Reorder $5$ and ${(x^{4})}^{2}$ .

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

Step 3.4

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

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot 5 x}$

Step 3.5

Add parentheses.

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot (5 x)}$

Step 4

Pull terms out from under the radical.

${(x^{2})}^{2} \sqrt{5 x}$

Step 5

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 5.1

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

$x^{2 \cdot 2} \sqrt{5 x}$

Step 5.2

Multiply $2$ by $2$ .

$x^{4} \sqrt{5 x}$