Basic Math Examples

$\frac{- 5 z^{5}}{4 z^{3}} \cdot \frac{16 z^{6}}{25 z}$

Step 1

Combine.

$\frac{- 5 z^{5} (16 z^{6})}{4 z^{3} (25 z)}$

Step 2

Multiply $z^{5}$ by $z^{6}$ by adding the exponents.

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Step 2.1

Move $z^{6}$ .

$\frac{- 5 (z^{6} z^{5}) \cdot 16}{4 z^{3} (25 z)}$

Step 2.2

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

$\frac{- 5 z^{6 + 5} \cdot 16}{4 z^{3} (25 z)}$

Step 2.3

Add $6$ and $5$ .

$\frac{- 5 z^{11} \cdot 16}{4 z^{3} (25 z)}$

Step 3

Multiply $z^{3}$ by $z$ by adding the exponents.

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Step 3.1

Move $z$ .

$\frac{- 5 z^{11} \cdot 16}{4 (z \cdot z^{3}) \cdot 25}$

Step 3.2

Multiply $z$ by $z^{3}$ .

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Step 3.2.1

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

$\frac{- 5 z^{11} \cdot 16}{4 (z^{1} z^{3}) \cdot 25}$

Step 3.2.2

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

$\frac{- 5 z^{11} \cdot 16}{4 z^{1 + 3} \cdot 25}$

Step 3.3

Add $1$ and $3$ .

$\frac{- 5 z^{11} \cdot 16}{4 z^{4} \cdot 25}$

Step 4

Cancel the common factor of $- 5$ and $25$ .

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Step 4.1

Factor $5$ out of $- 5 z^{11} \cdot 16$ .

$\frac{5 (- z^{11} \cdot 16)}{4 z^{4} \cdot 25}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $4 z^{4} \cdot 25$ .

$\frac{5 (- z^{11} \cdot 16)}{5 (4 z^{4} \cdot 5)}$

Step 4.2.2

Cancel the common factor.

$\frac{5 (- z^{11} \cdot 16)}{5 (4 z^{4} \cdot 5)}$

Step 4.2.3

Rewrite the expression.

$\frac{- z^{11} \cdot 16}{4 z^{4} \cdot 5}$

Step 5

Cancel the common factor of $z^{11}$ and $z^{4}$ .

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Step 5.1

Factor $z^{4}$ out of $- z^{11} \cdot 16$ .

$\frac{z^{4} (- z^{7} \cdot 16)}{4 z^{4} \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $z^{4}$ out of $4 z^{4} \cdot 5$ .

$\frac{z^{4} (- z^{7} \cdot 16)}{z^{4} (4 \cdot 5)}$

Step 5.2.2

Cancel the common factor.

$\frac{z^{4} (- z^{7} \cdot 16)}{z^{4} (4 \cdot 5)}$

Step 5.2.3

Rewrite the expression.

$\frac{- z^{7} \cdot 16}{4 \cdot 5}$

Step 6

Cancel the common factor of $16$ and $4$ .

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Step 6.1

Factor $4$ out of $- z^{7} \cdot 16$ .

$\frac{4 (- z^{7} \cdot 4)}{4 \cdot 5}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $4 \cdot 5$ .

$\frac{4 (- z^{7} \cdot 4)}{4 (5)}$

Step 6.2.2

Cancel the common factor.

$\frac{4 (- z^{7} \cdot 4)}{4 \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{- z^{7} \cdot 4}{5}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $4$ by $- 1$ .

$\frac{- 4 z^{7}}{5}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{4 z^{7}}{5}$