Linear Algebra Examples

$\frac{8}{\sqrt{56 - 7 x}}$

Step 1

Factor $7$ out of $56 - 7 x$ .

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Step 1.1

Factor $7$ out of $56$ .

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

Step 1.2

Factor $7$ out of $- 7 x$ .

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

Step 1.3

Factor $7$ out of $7 (8) + 7 (- x)$ .

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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Step 3.1

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

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

Step 3.2

Raise $\sqrt{7 (8 - x)}$ to the power of $1$ .

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

Step 3.3

Raise $\sqrt{7 (8 - x)}$ to the power of $1$ .

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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

Step 3.6

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

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 (8 - x)}$ as ${(7 (8 - x))}^{\frac{1}{2}}$ .

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

Step 3.6.2

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

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

Step 3.6.3

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

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

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

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

Step 3.6.4.2

Rewrite the expression.

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

Step 3.6.5

Simplify.

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