Algebra Examples

$\frac{3^{4} d^{- \frac{3}{4}}}{3^{2} d^{\frac{3}{4}}}$

Step 1

Move $d^{- \frac{3}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3^{4}}{3^{2} d^{\frac{3}{4}} d^{\frac{3}{4}}}$

Step 2

Multiply $d^{\frac{3}{4}}$ by $d^{\frac{3}{4}}$ by adding the exponents.

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Step 2.1

Move $d^{\frac{3}{4}}$ .

$\frac{3^{4}}{3^{2} (d^{\frac{3}{4}} d^{\frac{3}{4}})}$

Step 2.2

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

$\frac{3^{4}}{3^{2} d^{\frac{3}{4} + \frac{3}{4}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3^{4}}{3^{2} d^{\frac{3 + 3}{4}}}$

Step 2.4

Add $3$ and $3$ .

$\frac{3^{4}}{3^{2} d^{\frac{6}{4}}}$

Step 2.5

Cancel the common factor of $6$ and $4$ .

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Step 2.5.1

Factor $2$ out of $6$ .

$\frac{3^{4}}{3^{2} d^{\frac{2 (3)}{4}}}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $4$ .

$\frac{3^{4}}{3^{2} d^{\frac{2 \cdot 3}{2 \cdot 2}}}$

Step 2.5.2.2

Cancel the common factor.

$\frac{3^{4}}{3^{2} d^{\frac{2 \cdot 3}{2 \cdot 2}}}$

Step 2.5.2.3

Rewrite the expression.

$\frac{3^{4}}{3^{2} d^{\frac{3}{2}}}$

Step 3

Factor $3^{2}$ out of $3^{4}$ .

$\frac{3^{2} \cdot 3^{2}}{3^{2} d^{\frac{3}{2}}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $3^{2}$ out of $3^{2} d^{\frac{3}{2}}$ .

$\frac{3^{2} \cdot 3^{2}}{3^{2} (d^{\frac{3}{2}})}$

Step 4.2

Cancel the common factor.

$\frac{3^{2} \cdot 3^{2}}{3^{2} d^{\frac{3}{2}}}$

Step 4.3

Rewrite the expression.

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

Step 5

Raise $3$ to the power of $2$ .

$\frac{9}{d^{\frac{3}{2}}}$