Algebra Examples

$10 \sqrt{x^{15}} \cdot \sqrt{x^{9}}$

Step 1

Rewrite $x^{15}$ as ${(x^{7})}^{2} x$ .

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Step 1.1

Factor out $x^{14}$ .

$10 \sqrt{x^{14} x} \cdot \sqrt{x^{9}}$

Step 1.2

Rewrite $x^{14}$ as ${(x^{7})}^{2}$ .

$10 \sqrt{{(x^{7})}^{2} x} \cdot \sqrt{x^{9}}$

Step 2

Pull terms out from under the radical.

$10 (| x^{7} | \sqrt{x}) \cdot \sqrt{x^{9}}$

Step 3

Rewrite $x^{9}$ as ${(x^{4})}^{2} x$ .

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Step 3.1

Factor out $x^{8}$ .

$10 | x^{7} | \sqrt{x} \cdot \sqrt{x^{8} x}$

Step 3.2

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

$10 | x^{7} | \sqrt{x} \cdot \sqrt{{(x^{4})}^{2} x}$

Step 4

Pull terms out from under the radical.

$10 | x^{7} | \sqrt{x} \cdot (| x^{4} | \sqrt{x})$

Step 5

Remove non-negative terms from the absolute value.

$10 | x^{7} | \sqrt{x} \cdot (x^{4} \sqrt{x})$

Step 6

Multiply $10 | x^{7} | \sqrt{x} (x^{4} \sqrt{x})$ .

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Step 6.1

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

$10 | x^{7} | (x^{4} ({\sqrt{x}}^{1} \sqrt{x}))$

Step 6.2

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

$10 | x^{7} | (x^{4} ({\sqrt{x}}^{1} {\sqrt{x}}^{1}))$

Step 6.3

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

$10 | x^{7} | (x^{4} {\sqrt{x}}^{1 + 1})$

Step 6.4

Add $1$ and $1$ .

$10 | x^{7} | (x^{4} {\sqrt{x}}^{2})$

Step 7

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

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Step 7.1

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

$10 | x^{7} | (x^{4} {(x^{\frac{1}{2}})}^{2})$

Step 7.2

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

$10 | x^{7} | (x^{4} x^{\frac{1}{2} \cdot 2})$

Step 7.3

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

$10 | x^{7} | (x^{4} x^{\frac{2}{2}})$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$10 | x^{7} | (x^{4} x^{\frac{2}{2}})$

Step 7.4.2

Rewrite the expression.

$10 | x^{7} | (x^{4} x^{1})$

Step 7.5

Simplify.

$10 | x^{7} | (x^{4} x)$

Step 8

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

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Step 8.1

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

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Step 8.1.1

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

$10 | x^{7} | (x^{4} x^{1})$

Step 8.1.2

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

$10 | x^{7} | x^{4 + 1}$

Step 8.2

Add $4$ and $1$ .

$10 | x^{7} | x^{5}$

Step 9

Reorder factors in $10 | x^{7} | x^{5}$ .

$10 x^{5} | x^{7} |$