Algebra Examples

$7 x^{\frac{3}{2}} \cdot - 14 x^{\frac{1}{3}}$

Step 1

Rewrite using the commutative property of multiplication.

$7 \cdot - 14 x^{\frac{3}{2}} x^{\frac{1}{3}}$

Step 2

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

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Step 2.1

Move $x^{\frac{1}{3}}$ .

$7 \cdot - 14 (x^{\frac{1}{3}} x^{\frac{3}{2}})$

Step 2.2

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

$7 \cdot - 14 x^{\frac{1}{3} + \frac{3}{2}}$

Step 2.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \cdot - 14 x^{\frac{1}{3} \cdot \frac{2}{2} + \frac{3}{2}}$

Step 2.4

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

$7 \cdot - 14 x^{\frac{1}{3} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{3}{3}}$

Step 2.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

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

$7 \cdot - 14 x^{\frac{2}{3 \cdot 2} + \frac{3}{2} \cdot \frac{3}{3}}$

Step 2.5.2

Multiply $3$ by $2$ .

$7 \cdot - 14 x^{\frac{2}{6} + \frac{3}{2} \cdot \frac{3}{3}}$

Step 2.5.3

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

$7 \cdot - 14 x^{\frac{2}{6} + \frac{3 \cdot 3}{2 \cdot 3}}$

Step 2.5.4

Multiply $2$ by $3$ .

$7 \cdot - 14 x^{\frac{2}{6} + \frac{3 \cdot 3}{6}}$

Step 2.6

Combine the numerators over the common denominator.

$7 \cdot - 14 x^{\frac{2 + 3 \cdot 3}{6}}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $3$ by $3$ .

$7 \cdot - 14 x^{\frac{2 + 9}{6}}$

Step 2.7.2

Add $2$ and $9$ .

$7 \cdot - 14 x^{\frac{11}{6}}$

Step 3

Multiply $7$ by $- 14$ .

$- 98 x^{\frac{11}{6}}$