Finite Math Examples

$2 (3 x^{3} z^{- 2}) (- x^{- 7} z^{2})$

Step 1

Multiply $x^{3}$ by $x^{- 7}$ by adding the exponents.

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Step 1.1

Move $x^{- 7}$ .

$2 (3 (x^{- 7} x^{3}) z^{- 2}) (- 1 z^{2})$

Step 1.2

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

$2 (3 x^{- 7 + 3} z^{- 2}) (- 1 z^{2})$

Step 1.3

Add $- 7$ and $3$ .

$2 (3 x^{- 4} z^{- 2}) (- 1 z^{2})$

Step 2

Multiply $z^{- 2}$ by $z^{2}$ by adding the exponents.

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Step 2.1

Move $z^{2}$ .

$2 (3 x^{- 4} (z^{2} z^{- 2})) \cdot - 1$

Step 2.2

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

$2 (3 x^{- 4} z^{2 - 2}) \cdot - 1$

Step 2.3

Subtract $2$ from $2$ .

$2 (3 x^{- 4} z^{0}) \cdot - 1$

Step 3

Simplify $2 (3 x^{- 4} z^{0}) \cdot - 1$ .

$2 (3 x^{- 4}) \cdot - 1$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 (3 \frac{1}{x^{4}}) \cdot - 1$

Step 5

Combine $3$ and $\frac{1}{x^{4}}$ .

$2 \frac{3}{x^{4}} \cdot - 1$

Step 6

Multiply $2 \frac{3}{x^{4}}$ .

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Step 6.1

Combine $2$ and $\frac{3}{x^{4}}$ .

$\frac{2 \cdot 3}{x^{4}} \cdot - 1$

Step 6.2

Multiply $2$ by $3$ .

$\frac{6}{x^{4}} \cdot - 1$

Step 7

Multiply $\frac{6}{x^{4}} \cdot - 1$ .

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Step 7.1

Combine $\frac{6}{x^{4}}$ and $- 1$ .

$\frac{6 \cdot - 1}{x^{4}}$

Step 7.2

Multiply $6$ by $- 1$ .

$\frac{- 6}{x^{4}}$

Step 8

Move the negative in front of the fraction.

$- \frac{6}{x^{4}}$