Basic Math Examples

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

Step 1

Rewrite using the commutative property of multiplication.

$4 \cdot 5 z^{\frac{3}{4}} z^{\frac{2}{5}}$

Step 2

Multiply $z^{\frac{3}{4}}$ by $z^{\frac{2}{5}}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $z^{\frac{2}{5}}$ .

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

Step 2.2

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

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

Step 2.3

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.4

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.5

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.5.1

Multiply $\frac{2}{5}$ by $\frac{4}{4}$ .

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

Step 2.5.2

Multiply $5$ by $4$ .

$4 \cdot 5 z^{\frac{2 \cdot 4}{20} + \frac{3}{4} \cdot \frac{5}{5}}$

Step 2.5.3

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$4 \cdot 5 z^{\frac{2 \cdot 4}{20} + \frac{3 \cdot 5}{4 \cdot 5}}$

Step 2.5.4

Multiply $4$ by $5$ .

$4 \cdot 5 z^{\frac{2 \cdot 4}{20} + \frac{3 \cdot 5}{20}}$

Step 2.6

Combine the numerators over the common denominator.

$4 \cdot 5 z^{\frac{2 \cdot 4 + 3 \cdot 5}{20}}$

Step 2.7

Simplify the numerator.

Tap for more steps...

Step 2.7.1

Multiply $2$ by $4$ .

$4 \cdot 5 z^{\frac{8 + 3 \cdot 5}{20}}$

Step 2.7.2

Multiply $3$ by $5$ .

$4 \cdot 5 z^{\frac{8 + 15}{20}}$

Step 2.7.3

Add $8$ and $15$ .

$4 \cdot 5 z^{\frac{23}{20}}$

Step 3

Multiply $4$ by $5$ .

$20 z^{\frac{23}{20}}$