Algebra Examples

$4 x^{2} \sqrt{5 x^{4}} \cdot 3 \sqrt{5 x^{8}}$

Step 1

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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Step 1.1

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

$4 x^{2} \sqrt{5 {(x^{2})}^{2}} \cdot (3 \sqrt{5 x^{8}})$

Step 1.2

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

$4 x^{2} \sqrt{{(x^{2})}^{2} \cdot 5} \cdot (3 \sqrt{5 x^{8}})$

Step 2

Pull terms out from under the radical.

$4 x^{2} (x^{2} \sqrt{5}) \cdot (3 \sqrt{5 x^{8}})$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$4 (x^{2} x^{2}) \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

Step 3.2

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

$4 x^{2 + 2} \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

Step 3.3

Add $2$ and $2$ .

$4 x^{4} \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

Step 4

Rewrite $5 x^{8}$ as ${({(x^{2})}^{2})}^{2} \cdot 5$ .

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $2$ .

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

Step 7

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

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Step 7.1

Move $x^{4}$ .

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

Step 7.2

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

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

Step 7.3

Add $4$ and $4$ .

$4 x^{8} \sqrt{5} \cdot (3 (\sqrt{5}))$

Step 8

Multiply $4 x^{8} \sqrt{5} (3 \sqrt{5})$ .

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Step 8.1

Multiply $3$ by $4$ .

$12 x^{8} \sqrt{5} \sqrt{5}$

Step 8.2

Raise $\sqrt{5}$ to the power of $1$ .

$12 x^{8} ({\sqrt{5}}^{1} \sqrt{5})$

Step 8.3

Raise $\sqrt{5}$ to the power of $1$ .

$12 x^{8} ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

Step 8.4

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

$12 x^{8} {\sqrt{5}}^{1 + 1}$

Step 8.5

Add $1$ and $1$ .

$12 x^{8} {\sqrt{5}}^{2}$

Step 9

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 9.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$12 x^{8} {(5^{\frac{1}{2}})}^{2}$

Step 9.2

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

$12 x^{8} \cdot 5^{\frac{1}{2} \cdot 2}$

Step 9.3

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

$12 x^{8} \cdot 5^{\frac{2}{2}}$

Step 9.4

Cancel the common factor of $2$ .

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Step 9.4.1

Cancel the common factor.

$12 x^{8} \cdot 5^{\frac{2}{2}}$

Step 9.4.2

Rewrite the expression.

$12 x^{8} \cdot 5^{1}$

Step 9.5

Evaluate the exponent.

$12 x^{8} \cdot 5$

Step 10

Multiply $5$ by $12$ .

$60 x^{8}$