Basic Math Examples

$\sqrt{6} a^{2} b \cdot (\sqrt{42} a b^{3})$

Step 1

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

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Step 1.1

Move $a$ .

$\sqrt{6} (a \cdot a^{2}) b \cdot (\sqrt{42} b^{3})$

Step 1.2

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

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Step 1.2.1

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

$\sqrt{6} (a^{1} a^{2}) b \cdot (\sqrt{42} b^{3})$

Step 1.2.2

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

$\sqrt{6} a^{1 + 2} b \cdot (\sqrt{42} b^{3})$

Step 1.3

Add $1$ and $2$ .

$\sqrt{6} a^{3} b \cdot (\sqrt{42} b^{3})$

Step 2

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

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Step 2.1

Move $b^{3}$ .

$\sqrt{6} a^{3} (b^{3} b) \cdot \sqrt{42}$

Step 2.2

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

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Step 2.2.1

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

$\sqrt{6} a^{3} (b^{3} b^{1}) \cdot \sqrt{42}$

Step 2.2.2

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

$\sqrt{6} a^{3} b^{3 + 1} \cdot \sqrt{42}$

Step 2.3

Add $3$ and $1$ .

$\sqrt{6} a^{3} b^{4} \cdot \sqrt{42}$

Step 3

Multiply $\sqrt{6} a^{3} b^{4} \sqrt{42}$ .

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Step 3.1

Combine using the product rule for radicals.

$a^{3} b^{4} \sqrt{6 \cdot 42}$

Step 3.2

Multiply $6$ by $42$ .

$a^{3} b^{4} \sqrt{252}$

Step 4

Rewrite $252$ as $6^{2} \cdot 7$ .

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Step 4.1

Factor $36$ out of $252$ .

$a^{3} b^{4} \sqrt{36 (7)}$

Step 4.2

Rewrite $36$ as $6^{2}$ .

$a^{3} b^{4} \sqrt{6^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$a^{3} b^{4} (6 \sqrt{7})$

Step 6

Move $6$ to the left of $a^{3} b^{4}$ .

$6 a^{3} b^{4} \sqrt{7}$