Algebra Examples

$\sqrt{x^{\frac{3}{4}} x^{- 1}}$

Step 1

Multiply $x^{\frac{3}{4}}$ by $x^{- 1}$ by adding the exponents.

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Step 1.1

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

$\sqrt{x^{\frac{3}{4} - 1}}$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\sqrt{x^{\frac{3}{4} - 1 \cdot \frac{4}{4}}}$

Step 1.3

Combine $- 1$ and $\frac{4}{4}$ .

$\sqrt{x^{\frac{3}{4} + \frac{- 1 \cdot 4}{4}}}$

Step 1.4

Combine the numerators over the common denominator.

$\sqrt{x^{\frac{3 - 1 \cdot 4}{4}}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $4$ .

$\sqrt{x^{\frac{3 - 4}{4}}}$

Step 1.5.2

Subtract $4$ from $3$ .

$\sqrt{x^{\frac{- 1}{4}}}$

Step 1.6

Move the negative in front of the fraction.

$\sqrt{x^{- \frac{1}{4}}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt{\frac{1}{x^{\frac{1}{4}}}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{\frac{1}{\sqrt[4]{x^{1}}}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt{\frac{1}{\sqrt[4]{x}}}$