Pre-Algebra Examples

$\frac{3^{\frac{1}{2}} \cdot 3^{\frac{3}{4}}}{3^{\frac{1}{4}}}$

Step 1

Multiply $3^{\frac{1}{2}}$ by $3^{\frac{3}{4}}$ 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.

$\frac{3^{\frac{1}{2} + \frac{3}{4}}}{3^{\frac{1}{4}}}$

Step 1.2

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

$\frac{3^{\frac{1}{2} \cdot \frac{2}{2} + \frac{3}{4}}}{3^{\frac{1}{4}}}$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{3^{\frac{2}{2 \cdot 2} + \frac{3}{4}}}{3^{\frac{1}{4}}}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3^{\frac{2}{4} + \frac{3}{4}}}{3^{\frac{1}{4}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3^{\frac{2 + 3}{4}}}{3^{\frac{1}{4}}}$

Step 1.5

Add $2$ and $3$ .

$\frac{3^{\frac{5}{4}}}{3^{\frac{1}{4}}}$

Step 2

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

$3^{\frac{5}{4}} \cdot 3^{- \frac{1}{4}}$

Step 3

Multiply $3^{\frac{5}{4}}$ by $3^{- \frac{1}{4}}$ by adding the exponents.

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Step 3.1

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

$3^{\frac{5}{4} - \frac{1}{4}}$

Step 3.2

Combine the numerators over the common denominator.

$3^{\frac{5 - 1}{4}}$

Step 3.3

Subtract $1$ from $5$ .

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

Step 3.4

Divide $4$ by $4$ .

$3^{1}$

Step 4

Simplify $3^{1}$ .

$3$