Basic Math Examples

$\frac{9 a^{5} z}{z^{4}} \cdot \frac{3 a^{3}}{5 z}$

Step 1

Combine.

$\frac{9 a^{5} z (3 a^{3})}{z^{4} (5 z)}$

Step 2

Multiply $a^{5}$ by $a^{3}$ by adding the exponents.

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Step 2.1

Move $a^{3}$ .

$\frac{9 (a^{3} a^{5}) z \cdot 3}{z^{4} (5 z)}$

Step 2.2

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

$\frac{9 a^{3 + 5} z \cdot 3}{z^{4} (5 z)}$

Step 2.3

Add $3$ and $5$ .

$\frac{9 a^{8} z \cdot 3}{z^{4} (5 z)}$

Step 3

Multiply $z^{4}$ by $z$ by adding the exponents.

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Step 3.1

Move $z$ .

$\frac{9 a^{8} z \cdot 3}{z \cdot z^{4} \cdot 5}$

Step 3.2

Multiply $z$ by $z^{4}$ .

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Step 3.2.1

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

$\frac{9 a^{8} z \cdot 3}{z^{1} z^{4} \cdot 5}$

Step 3.2.2

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

$\frac{9 a^{8} z \cdot 3}{z^{1 + 4} \cdot 5}$

Step 3.3

Add $1$ and $4$ .

$\frac{9 a^{8} z \cdot 3}{z^{5} \cdot 5}$

Step 4

Cancel the common factor of $z$ and $z^{5}$ .

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Step 4.1

Factor $z$ out of $9 a^{8} z \cdot 3$ .

$\frac{z (9 a^{8} \cdot 3)}{z^{5} \cdot 5}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $z$ out of $z^{5} \cdot 5$ .

$\frac{z (9 a^{8} \cdot 3)}{z (z^{4} \cdot 5)}$

Step 4.2.2

Cancel the common factor.

$\frac{z (9 a^{8} \cdot 3)}{z (z^{4} \cdot 5)}$

Step 4.2.3

Rewrite the expression.

$\frac{9 a^{8} \cdot 3}{z^{4} \cdot 5}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $3$ by $9$ .

$\frac{27 a^{8}}{z^{4} \cdot 5}$

Step 5.2

Move $5$ to the left of $z^{4}$ .

$\frac{27 a^{8}}{5 z^{4}}$