Precalculus Examples

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{1}{\sqrt{x}})}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$x^{\frac{3}{2} \cdot (\sqrt{x} - (\frac{1}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}))}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{1}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Step 1.2.2

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

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}})}$

Step 1.2.3

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

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}})}$

Step 1.2.4

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

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{{\sqrt{x}}^{1 + 1}})}$

Step 1.2.5

Add $1$ and $1$ .

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

Step 1.2.6

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

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Step 1.2.6.1

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

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{{(x^{\frac{1}{2}})}^{2}})}$

Step 1.2.6.2

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

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{x^{\frac{1}{2} \cdot 2}})}$

Step 1.2.6.3

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

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

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

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

Step 1.2.6.4.2

Rewrite the expression.

$x^{\frac{3}{2} \cdot (\sqrt{x} - \frac{\sqrt{x}}{x^{1}})}$

Step 1.2.6.5

Simplify.

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$x^{\frac{3}{2} \sqrt{x} + \frac{3}{2} (- \frac{\sqrt{x}}{x})}$

Step 2.2

Combine $\frac{3}{2}$ and $\sqrt{x}$ .

$x^{\frac{3 \sqrt{x}}{2} + \frac{3}{2} (- \frac{\sqrt{x}}{x})}$

Step 2.3

Multiply $\frac{3}{2}$ by $\frac{\sqrt{x}}{x}$ .

$x^{\frac{3 \sqrt{x}}{2} - \frac{3 \sqrt{x}}{2 x}}$