Algebra Examples

$(3 \sqrt{7 a^{2} b}) (5 a \sqrt{7 b})$

Step 1

Rewrite $7 a^{2} b$ as $a^{2} \cdot (7 b)$ .

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Step 1.1

Reorder $7$ and $a^{2}$ .

$3 \sqrt{a^{2} \cdot 7 b} (5 a \sqrt{7 b})$

Step 1.2

Add parentheses.

$3 \sqrt{a^{2} \cdot (7 b)} (5 a \sqrt{7 b})$

Step 2

Pull terms out from under the radical.

$3 (a \sqrt{7 b}) (5 a \sqrt{7 b})$

Step 3

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1

Move $a$ .

$3 (a \cdot a \sqrt{7 b}) (5 \sqrt{7 b})$

Step 3.2

Multiply $a$ by $a$ .

$3 (a^{2} \sqrt{7 b}) (5 \sqrt{7 b})$

Step 4

Multiply $3 a^{2} \sqrt{7 b} (5 \sqrt{7 b})$ .

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Step 4.1

Multiply $5$ by $3$ .

$15 a^{2} \sqrt{7 b} \sqrt{7 b}$

Step 4.2

Raise $\sqrt{7 b}$ to the power of $1$ .

$15 a^{2} ({\sqrt{7 b}}^{1} \sqrt{7 b})$

Step 4.3

Raise $\sqrt{7 b}$ to the power of $1$ .

$15 a^{2} ({\sqrt{7 b}}^{1} {\sqrt{7 b}}^{1})$

Step 4.4

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

$15 a^{2} {\sqrt{7 b}}^{1 + 1}$

Step 4.5

Add $1$ and $1$ .

$15 a^{2} {\sqrt{7 b}}^{2}$

Step 5

Rewrite ${\sqrt{7 b}}^{2}$ as $7 b$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 b}$ as ${(7 b)}^{\frac{1}{2}}$ .

$15 a^{2} {({(7 b)}^{\frac{1}{2}})}^{2}$

Step 5.2

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

$15 a^{2} {(7 b)}^{\frac{1}{2} \cdot 2}$

Step 5.3

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

$15 a^{2} {(7 b)}^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$15 a^{2} {(7 b)}^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

$15 a^{2} {(7 b)}^{1}$

Step 5.5

Simplify.

$15 a^{2} (7 b)$

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$15 \cdot 7 a^{2} b$

Step 6.2

Multiply $15$ by $7$ .

$105 a^{2} b$