Algebra Examples

$- 4 \sqrt{28 x} \cdot \sqrt{7 x^{3}}$

Step 1

Rewrite $28 x$ as $2^{2} \cdot (7 x)$ .

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Step 1.1

Factor $4$ out of $28$ .

$- 4 \sqrt{4 (7) x} \cdot \sqrt{7 x^{3}}$

Step 1.2

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

$- 4 \sqrt{2^{2} \cdot 7 x} \cdot \sqrt{7 x^{3}}$

Step 1.3

Add parentheses.

$- 4 \sqrt{2^{2} \cdot (7 x)} \cdot \sqrt{7 x^{3}}$

Step 2

Pull terms out from under the radical.

$- 4 (2 \sqrt{7 x}) \cdot \sqrt{7 x^{3}}$

Step 3

Multiply $2$ by $- 4$ .

$- 8 \sqrt{7 x} \cdot \sqrt{7 x^{3}}$

Step 4

Rewrite $7 x^{3}$ as $x^{2} \cdot (7 x)$ .

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Step 4.1

Factor out $x^{2}$ .

$- 8 \sqrt{7 x} \cdot \sqrt{7 (x^{2} x)}$

Step 4.2

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

$- 8 \sqrt{7 x} \cdot \sqrt{x^{2} \cdot 7 x}$

Step 4.3

Add parentheses.

$- 8 \sqrt{7 x} \cdot \sqrt{x^{2} \cdot (7 x)}$

Step 5

Pull terms out from under the radical.

$- 8 \sqrt{7 x} \cdot (x \sqrt{7 x})$

Step 6

Multiply $- 8 \sqrt{7 x} (x \sqrt{7 x})$ .

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Step 6.1

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

$- 8 (x ({\sqrt{7 x}}^{1} \sqrt{7 x}))$

Step 6.2

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

$- 8 (x ({\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1}))$

Step 6.3

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

$- 8 (x {\sqrt{7 x}}^{1 + 1})$

Step 6.4

Add $1$ and $1$ .

$- 8 (x {\sqrt{7 x}}^{2})$

Step 7

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

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Step 7.1

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

$- 8 (x {({(7 x)}^{\frac{1}{2}})}^{2})$

Step 7.2

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

$- 8 (x {(7 x)}^{\frac{1}{2} \cdot 2})$

Step 7.3

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

$- 8 (x {(7 x)}^{\frac{2}{2}})$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$- 8 (x {(7 x)}^{\frac{2}{2}})$

Step 7.4.2

Rewrite the expression.

$- 8 (x {(7 x)}^{1})$

Step 7.5

Simplify.

$- 8 (x (7 x))$

Step 8

Multiply $x$ by $x$ by adding the exponents.

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Step 8.1

Move $x$ .

$- 8 (x \cdot x \cdot 7)$

Step 8.2

Multiply $x$ by $x$ .

$- 8 (x^{2} \cdot 7)$

Step 9

Move $7$ to the left of $x^{2}$ .

$- 8 (7 \cdot x^{2})$

Step 10

Multiply $7$ by $- 8$ .

$- 56 x^{2}$