Algebra Examples

$(\sqrt{16 x^{5}}) (5 \sqrt{9 x^{3}})$

Step 1

Rewrite using the commutative property of multiplication.

$5 \sqrt{16 x^{5}} \sqrt{9 x^{3}}$

Step 2

Rewrite $16 x^{5}$ as ${(4 x^{2})}^{2} x$ .

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$5 \sqrt{4^{2} x^{5}} \sqrt{9 x^{3}}$

Step 2.2

Factor out $x^{4}$ .

$5 \sqrt{4^{2} (x^{4} x)} \sqrt{9 x^{3}}$

Step 2.3

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

$5 \sqrt{4^{2} ({(x^{2})}^{2} x)} \sqrt{9 x^{3}}$

Step 2.4

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

$5 \sqrt{{(4 x^{2})}^{2} x} \sqrt{9 x^{3}}$

Step 3

Pull terms out from under the radical.

$5 (4 x^{2} \sqrt{x}) \sqrt{9 x^{3}}$

Step 4

Multiply $4$ by $5$ .

$20 (x^{2} \sqrt{x}) \sqrt{9 x^{3}}$

Step 5

Rewrite $9 x^{3}$ as ${(3 x)}^{2} x$ .

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Step 5.1

Rewrite $9$ as $3^{2}$ .

$20 x^{2} \sqrt{x} \sqrt{3^{2} x^{3}}$

Step 5.2

Factor out $x^{2}$ .

$20 x^{2} \sqrt{x} \sqrt{3^{2} (x^{2} x)}$

Step 5.3

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$20 x^{2} \sqrt{x} \sqrt{{(3 x)}^{2} x}$

Step 6

Pull terms out from under the radical.

$20 x^{2} \sqrt{x} (3 x \sqrt{x})$

Step 7

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

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Step 7.1

Move $x$ .

$20 (x \cdot x^{2}) \sqrt{x} (3 \sqrt{x})$

Step 7.2

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

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Step 7.2.1

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

$20 (x^{1} x^{2}) \sqrt{x} (3 \sqrt{x})$

Step 7.2.2

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

$20 x^{1 + 2} \sqrt{x} (3 \sqrt{x})$

Step 7.3

Add $1$ and $2$ .

$20 x^{3} \sqrt{x} (3 \sqrt{x})$

Step 8

Multiply $20 x^{3} \sqrt{x} (3 \sqrt{x})$ .

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Step 8.1

Multiply $3$ by $20$ .

$60 x^{3} \sqrt{x} \sqrt{x}$

Step 8.2

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

$60 x^{3} ({\sqrt{x}}^{1} \sqrt{x})$

Step 8.3

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

$60 x^{3} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

Step 8.4

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

$60 x^{3} {\sqrt{x}}^{1 + 1}$

Step 8.5

Add $1$ and $1$ .

$60 x^{3} {\sqrt{x}}^{2}$

Step 9

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

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Step 9.1

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

$60 x^{3} {(x^{\frac{1}{2}})}^{2}$

Step 9.2

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

$60 x^{3} x^{\frac{1}{2} \cdot 2}$

Step 9.3

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

$60 x^{3} x^{\frac{2}{2}}$

Step 9.4

Cancel the common factor of $2$ .

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Step 9.4.1

Cancel the common factor.

$60 x^{3} x^{\frac{2}{2}}$

Step 9.4.2

Rewrite the expression.

$60 x^{3} x^{1}$

Step 9.5

Simplify.

$60 x^{3} x$

Step 10

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 10.1

Move $x$ .

$60 (x \cdot x^{3})$

Step 10.2

Multiply $x$ by $x^{3}$ .

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Step 10.2.1

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

$60 (x^{1} x^{3})$

Step 10.2.2

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

$60 x^{1 + 3}$

Step 10.3

Add $1$ and $3$ .

$60 x^{4}$