Pre-Algebra Examples

$(8 x^{\frac{1}{5}}) (3 x^{\frac{1}{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$8 \cdot 3 x^{\frac{1}{5}} x^{\frac{1}{2}}$

Step 2

Multiply $x^{\frac{1}{5}}$ by $x^{\frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $x^{\frac{1}{2}}$ .

$8 \cdot 3 (x^{\frac{1}{2}} x^{\frac{1}{5}})$

Step 2.2

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

$8 \cdot 3 x^{\frac{1}{2} + \frac{1}{5}}$

Step 2.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 \cdot 3 x^{\frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5}}$

Step 2.4

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 \cdot 3 x^{\frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{2}{2}}$

Step 2.5

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.5.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$8 \cdot 3 x^{\frac{5}{2 \cdot 5} + \frac{1}{5} \cdot \frac{2}{2}}$

Step 2.5.2

Multiply $2$ by $5$ .

$8 \cdot 3 x^{\frac{5}{10} + \frac{1}{5} \cdot \frac{2}{2}}$

Step 2.5.3

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$8 \cdot 3 x^{\frac{5}{10} + \frac{2}{5 \cdot 2}}$

Step 2.5.4

Multiply $5$ by $2$ .

$8 \cdot 3 x^{\frac{5}{10} + \frac{2}{10}}$

Step 2.6

Combine the numerators over the common denominator.

$8 \cdot 3 x^{\frac{5 + 2}{10}}$

Step 2.7

Add $5$ and $2$ .

$8 \cdot 3 x^{\frac{7}{10}}$

Step 3

Multiply $8$ by $3$ .

$24 x^{\frac{7}{10}}$