Pre-Algebra Examples

$\frac{4}{z^{2} w^{5}} + \frac{9}{z^{3} w^{3}}$

Step 1

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

$\frac{4}{z^{2} w^{5}} \cdot \frac{z}{z} + \frac{9}{z^{3} w^{3}}$

Step 2

To write $\frac{9}{z^{3} w^{3}}$ as a fraction with a common denominator, multiply by $\frac{w^{2}}{w^{2}}$ .

$\frac{4}{z^{2} w^{5}} \cdot \frac{z}{z} + \frac{9}{z^{3} w^{3}} \cdot \frac{w^{2}}{w^{2}}$

Step 3

Write each expression with a common denominator of $z^{3} w^{5}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{z^{2} w^{5}}$ by $\frac{z}{z}$ .

$\frac{4 z}{z^{2} w^{5} z} + \frac{9}{z^{3} w^{3}} \cdot \frac{w^{2}}{w^{2}}$

Step 3.2

Raise $z$ to the power of $1$ .

$\frac{4 z}{w^{5} (z^{2} z^{1})} + \frac{9}{z^{3} w^{3}} \cdot \frac{w^{2}}{w^{2}}$

Step 3.3

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

$\frac{4 z}{w^{5} z^{2 + 1}} + \frac{9}{z^{3} w^{3}} \cdot \frac{w^{2}}{w^{2}}$

Step 3.4

Add $2$ and $1$ .

$\frac{4 z}{w^{5} z^{3}} + \frac{9}{z^{3} w^{3}} \cdot \frac{w^{2}}{w^{2}}$

Step 3.5

Multiply $\frac{9}{z^{3} w^{3}}$ by $\frac{w^{2}}{w^{2}}$ .

$\frac{4 z}{w^{5} z^{3}} + \frac{9 w^{2}}{z^{3} w^{3} w^{2}}$

Step 3.6

Multiply $w^{3}$ by $w^{2}$ by adding the exponents.

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Step 3.6.1

Move $w^{2}$ .

$\frac{4 z}{w^{5} z^{3}} + \frac{9 w^{2}}{z^{3} (w^{2} w^{3})}$

Step 3.6.2

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

$\frac{4 z}{w^{5} z^{3}} + \frac{9 w^{2}}{z^{3} w^{2 + 3}}$

Step 3.6.3

Add $2$ and $3$ .

$\frac{4 z}{w^{5} z^{3}} + \frac{9 w^{2}}{z^{3} w^{5}}$

Step 3.7

Reorder the factors of $z^{3} w^{5}$ .

$\frac{4 z}{w^{5} z^{3}} + \frac{9 w^{2}}{w^{5} z^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 z + 9 w^{2}}{w^{5} z^{3}}$