Algebra Examples

$\frac{(3 x)}{{(3 x)}^{\frac{3}{2}}}$

Step 1

Apply the product rule to $3 x$ .

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

Step 2

Move $x^{1}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{3}{3^{\frac{3}{2}} x^{\frac{3}{2}} x^{- 1}}$

Step 3

Move $3^{1}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

Step 4

Simplify the denominator.

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Step 4.1

Multiply $x^{\frac{3}{2}}$ by $x^{- 1}$ by adding the exponents.

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Step 4.1.1

Move $x^{- 1}$ .

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

Step 4.1.2

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

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

Step 4.1.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.1.4

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

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

Step 4.1.5

Combine the numerators over the common denominator.

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

Step 4.1.6

Simplify the numerator.

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Step 4.1.6.1

Multiply $- 1$ by $2$ .

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

Step 4.1.6.2

Add $- 2$ and $3$ .

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

Step 4.2

Multiply $3^{\frac{3}{2}}$ by $3^{- 1}$ by adding the exponents.

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Step 4.2.1

Move $3^{- 1}$ .

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

Step 4.2.2

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

$\frac{1}{3^{- 1 + \frac{3}{2}} x^{\frac{1}{2}}}$

Step 4.2.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.4

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

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

Step 4.2.5

Combine the numerators over the common denominator.

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

Step 4.2.6

Simplify the numerator.

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Step 4.2.6.1

Multiply $- 1$ by $2$ .

$\frac{1}{3^{\frac{- 2 + 3}{2}} x^{\frac{1}{2}}}$

Step 4.2.6.2

Add $- 2$ and $3$ .

$\frac{1}{3^{\frac{1}{2}} x^{\frac{1}{2}}}$