Precalculus Examples

$(- 2 a^{\frac{3}{4}}) (5 a^{\frac{3}{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$- 2 \cdot 5 a^{\frac{3}{4}} a^{\frac{3}{2}}$

Step 2

Multiply $a^{\frac{3}{4}}$ by $a^{\frac{3}{2}}$ by adding the exponents.

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Step 2.1

Move $a^{\frac{3}{2}}$ .

$- 2 \cdot 5 (a^{\frac{3}{2}} a^{\frac{3}{4}})$

Step 2.2

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

$- 2 \cdot 5 a^{\frac{3}{2} + \frac{3}{4}}$

Step 2.3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 \cdot 5 a^{\frac{3}{2} \cdot \frac{2}{2} + \frac{3}{4}}$

Step 2.4

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

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Step 2.4.1

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

$- 2 \cdot 5 a^{\frac{3 \cdot 2}{2 \cdot 2} + \frac{3}{4}}$

Step 2.4.2

Multiply $2$ by $2$ .

$- 2 \cdot 5 a^{\frac{3 \cdot 2}{4} + \frac{3}{4}}$

Step 2.5

Combine the numerators over the common denominator.

$- 2 \cdot 5 a^{\frac{3 \cdot 2 + 3}{4}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $2$ .

$- 2 \cdot 5 a^{\frac{6 + 3}{4}}$

Step 2.6.2

Add $6$ and $3$ .

$- 2 \cdot 5 a^{\frac{9}{4}}$

Step 3

Multiply $- 2$ by $5$ .

$- 10 a^{\frac{9}{4}}$