Algebra Examples

$2 \sqrt{8 b^{3}} \cdot 9 \sqrt{18 b}$

Step 1

Rewrite $8 b^{3}$ as ${(2 b)}^{2} \cdot (2 b)$ .

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Step 1.1

Factor $4$ out of $8$ .

$2 \sqrt{4 (2) b^{3}} \cdot (9 \sqrt{18 b})$

Step 1.2

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

$2 \sqrt{2^{2} \cdot 2 b^{3}} \cdot (9 \sqrt{18 b})$

Step 1.3

Factor out $b^{2}$ .

$2 \sqrt{2^{2} \cdot 2 (b^{2} b)} \cdot (9 \sqrt{18 b})$

Step 1.4

Move $2$ .

$2 \sqrt{2^{2} b^{2} \cdot 2 b} \cdot (9 \sqrt{18 b})$

Step 1.5

Rewrite $2^{2} b^{2}$ as ${(2 b)}^{2}$ .

$2 \sqrt{{(2 b)}^{2} \cdot 2 b} \cdot (9 \sqrt{18 b})$

Step 1.6

Add parentheses.

$2 \sqrt{{(2 b)}^{2} \cdot (2 b)} \cdot (9 \sqrt{18 b})$

Step 2

Pull terms out from under the radical.

$2 (2 b \sqrt{2 b}) \cdot (9 \sqrt{18 b})$

Step 3

Multiply $2$ by $2$ .

$4 (b \sqrt{2 b}) \cdot (9 \sqrt{18 b})$

Step 4

Rewrite $18 b$ as $3^{2} \cdot (2 b)$ .

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Step 4.1

Factor $9$ out of $18$ .

$4 b \sqrt{2 b} \cdot (9 \sqrt{9 (2) b})$

Step 4.2

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

$4 b \sqrt{2 b} \cdot (9 \sqrt{3^{2} \cdot 2 b})$

Step 4.3

Add parentheses.

$4 b \sqrt{2 b} \cdot (9 \sqrt{3^{2} \cdot (2 b)})$

Step 5

Pull terms out from under the radical.

$4 b \sqrt{2 b} \cdot (9 (3 \sqrt{2 b}))$

Step 6

Multiply $3$ by $9$ .

$4 b \sqrt{2 b} \cdot (27 \sqrt{2 b})$

Step 7

Multiply $4 b \sqrt{2 b} (27 \sqrt{2 b})$ .

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Step 7.1

Multiply $27$ by $4$ .

$108 b \sqrt{2 b} \sqrt{2 b}$

Step 7.2

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

$108 b ({\sqrt{2 b}}^{1} \sqrt{2 b})$

Step 7.3

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

$108 b ({\sqrt{2 b}}^{1} {\sqrt{2 b}}^{1})$

Step 7.4

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

$108 b {\sqrt{2 b}}^{1 + 1}$

Step 7.5

Add $1$ and $1$ .

$108 b {\sqrt{2 b}}^{2}$

Step 8

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

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Step 8.1

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

$108 b {({(2 b)}^{\frac{1}{2}})}^{2}$

Step 8.2

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

$108 b {(2 b)}^{\frac{1}{2} \cdot 2}$

Step 8.3

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

$108 b {(2 b)}^{\frac{2}{2}}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Cancel the common factor.

$108 b {(2 b)}^{\frac{2}{2}}$

Step 8.4.2

Rewrite the expression.

$108 b {(2 b)}^{1}$

Step 8.5

Simplify.

$108 b (2 b)$

Step 9

Rewrite using the commutative property of multiplication.

$108 \cdot 2 b \cdot b$

Step 10

Multiply $b$ by $b$ by adding the exponents.

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Step 10.1

Move $b$ .

$108 \cdot 2 (b \cdot b)$

Step 10.2

Multiply $b$ by $b$ .

$108 \cdot 2 b^{2}$

Step 11

Multiply $108$ by $2$ .

$216 b^{2}$