Basic Math Examples

$- 3 q \sqrt{2} \cdot (q \sqrt{8})$

Step 1

Multiply $q$ by $q$ by adding the exponents.

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Step 1.1

Move $q$ .

$- 3 (q \cdot q) \sqrt{2} \cdot \sqrt{8}$

Step 1.2

Multiply $q$ by $q$ .

$- 3 q^{2} \sqrt{2} \cdot \sqrt{8}$

Step 2

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 2.1

Factor $4$ out of $8$ .

$- 3 q^{2} \sqrt{2} \cdot \sqrt{4 (2)}$

Step 2.2

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

$- 3 q^{2} \sqrt{2} \cdot \sqrt{2^{2} \cdot 2}$

Step 3

Pull terms out from under the radical.

$- 3 q^{2} \sqrt{2} \cdot (2 \sqrt{2})$

Step 4

Multiply $- 3 q^{2} \sqrt{2} (2 \sqrt{2})$ .

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Step 4.1

Multiply $2$ by $- 3$ .

$- 6 q^{2} \sqrt{2} \sqrt{2}$

Step 4.2

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

$- 6 q^{2} ({\sqrt{2}}^{1} \sqrt{2})$

Step 4.3

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

$- 6 q^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 4.4

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

$- 6 q^{2} {\sqrt{2}}^{1 + 1}$

Step 4.5

Add $1$ and $1$ .

$- 6 q^{2} {\sqrt{2}}^{2}$

Step 5

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

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Step 5.1

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

$- 6 q^{2} {(2^{\frac{1}{2}})}^{2}$

Step 5.2

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

$- 6 q^{2} \cdot 2^{\frac{1}{2} \cdot 2}$

Step 5.3

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

$- 6 q^{2} \cdot 2^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$- 6 q^{2} \cdot 2^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

$- 6 q^{2} \cdot 2^{1}$

Step 5.5

Evaluate the exponent.

$- 6 q^{2} \cdot 2$

Step 6

Multiply $2$ by $- 6$ .

$- 12 q^{2}$