Algebra Examples

$5 \sqrt{8 x} \cdot 3 \sqrt{2 x^{5}}$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

$5 \sqrt{4 (2) x} \cdot (3 \sqrt{2 x^{5}})$

Step 1.2

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

$5 \sqrt{2^{2} \cdot 2 x} \cdot (3 \sqrt{2 x^{5}})$

Step 1.3

Add parentheses.

$5 \sqrt{2^{2} \cdot (2 x)} \cdot (3 \sqrt{2 x^{5}})$

Step 2

Pull terms out from under the radical.

$5 (2 \sqrt{2 x}) \cdot (3 \sqrt{2 x^{5}})$

Step 3

Multiply $2$ by $5$ .

$10 \sqrt{2 x} \cdot (3 \sqrt{2 x^{5}})$

Step 4

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

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Step 4.1

Factor out $x^{4}$ .

$10 \sqrt{2 x} \cdot (3 \sqrt{2 (x^{4} x)})$

Step 4.2

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

$10 \sqrt{2 x} \cdot (3 \sqrt{2 ({(x^{2})}^{2} x)})$

Step 4.3

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

$10 \sqrt{2 x} \cdot (3 \sqrt{{(x^{2})}^{2} \cdot 2 x})$

Step 4.4

Add parentheses.

$10 \sqrt{2 x} \cdot (3 \sqrt{{(x^{2})}^{2} \cdot (2 x)})$

Step 5

Pull terms out from under the radical.

$10 \sqrt{2 x} \cdot (3 (x^{2} \sqrt{2 x}))$

Step 6

Multiply $10 \sqrt{2 x} (3 x^{2} \sqrt{2 x})$ .

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Step 6.1

Multiply $3$ by $10$ .

$30 \sqrt{2 x} (x^{2} \sqrt{2 x})$

Step 6.2

Raise $\sqrt{2 x}$ to the power of $1$ .

$30 (x^{2} ({\sqrt{2 x}}^{1} \sqrt{2 x}))$

Step 6.3

Raise $\sqrt{2 x}$ to the power of $1$ .

$30 (x^{2} ({\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}))$

Step 6.4

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

$30 (x^{2} {\sqrt{2 x}}^{1 + 1})$

Step 6.5

Add $1$ and $1$ .

$30 (x^{2} {\sqrt{2 x}}^{2})$

Step 7

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

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Step 7.1

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

$30 (x^{2} {({(2 x)}^{\frac{1}{2}})}^{2})$

Step 7.2

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

$30 (x^{2} {(2 x)}^{\frac{1}{2} \cdot 2})$

Step 7.3

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

$30 (x^{2} {(2 x)}^{\frac{2}{2}})$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$30 (x^{2} {(2 x)}^{\frac{2}{2}})$

Step 7.4.2

Rewrite the expression.

$30 (x^{2} {(2 x)}^{1})$

Step 7.5

Simplify.

$30 (x^{2} (2 x))$

Step 8

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

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Step 8.1

Move $x$ .

$30 (x \cdot x^{2} \cdot 2)$

Step 8.2

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

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Step 8.2.1

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

$30 (x^{1} x^{2} \cdot 2)$

Step 8.2.2

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

$30 (x^{1 + 2} \cdot 2)$

Step 8.3

Add $1$ and $2$ .

$30 (x^{3} \cdot 2)$

Step 9

Move $2$ to the left of $x^{3}$ .

$30 (2 \cdot x^{3})$

Step 10

Multiply $2$ by $30$ .

$60 x^{3}$