Algebra Examples

$8 x^{- 9} + (- 3 x^{- 3} y^{- 2}) (\frac{5}{x^{6} y^{- 2}})$

Step 1

Simplify each term.

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Step 1.1

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

$8 \frac{1}{x^{9}} + (- 3 x^{- 3} y^{- 2}) (\frac{5}{x^{6} y^{- 2}})$

Step 1.2

Combine $8$ and $\frac{1}{x^{9}}$ .

$\frac{8}{x^{9}} + (- 3 x^{- 3} y^{- 2}) (\frac{5}{x^{6} y^{- 2}})$

Step 1.3

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

$\frac{8}{x^{9}} - 3 x^{- 3} y^{- 2} \frac{5}{x^{6} \frac{1}{y^{2}}}$

Step 1.4

Combine $x^{6}$ and $\frac{1}{y^{2}}$ .

$\frac{8}{x^{9}} - 3 x^{- 3} y^{- 2} \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.5

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

$\frac{8}{x^{9}} - 3 \frac{1}{x^{3}} y^{- 2} \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.6

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

$\frac{8}{x^{9}} + \frac{- 3}{x^{3}} y^{- 2} \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.7

Move the negative in front of the fraction.

$\frac{8}{x^{9}} - \frac{3}{x^{3}} y^{- 2} \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.8

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

$\frac{8}{x^{9}} - \frac{3}{x^{3}} \cdot \frac{1}{y^{2}} \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.9

Multiply $\frac{1}{y^{2}}$ by $\frac{3}{x^{3}}$ .

$\frac{8}{x^{9}} - \frac{3}{y^{2} x^{3}} \cdot \frac{5}{\frac{x^{6}}{y^{2}}}$

Step 1.10

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{x^{9}} - \frac{3}{y^{2} x^{3}} (5 \frac{y^{2}}{x^{6}})$

Step 1.11

Combine $5$ and $\frac{y^{2}}{x^{6}}$ .

$\frac{8}{x^{9}} - \frac{3}{y^{2} x^{3}} \cdot \frac{5 y^{2}}{x^{6}}$

Step 1.12

Cancel the common factor of $y^{2}$ .

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Step 1.12.1

Move the leading negative in $- \frac{3}{y^{2} x^{3}}$ into the numerator.

$\frac{8}{x^{9}} + \frac{- 3}{y^{2} x^{3}} \cdot \frac{5 y^{2}}{x^{6}}$

Step 1.12.2

Factor $y^{2}$ out of $y^{2} x^{3}$ .

$\frac{8}{x^{9}} + \frac{- 3}{y^{2} (x^{3})} \cdot \frac{5 y^{2}}{x^{6}}$

Step 1.12.3

Factor $y^{2}$ out of $5 y^{2}$ .

$\frac{8}{x^{9}} + \frac{- 3}{y^{2} (x^{3})} \cdot \frac{y^{2} \cdot 5}{x^{6}}$

Step 1.12.4

Cancel the common factor.

$\frac{8}{x^{9}} + \frac{- 3}{y^{2} x^{3}} \cdot \frac{y^{2} \cdot 5}{x^{6}}$

Step 1.12.5

Rewrite the expression.

$\frac{8}{x^{9}} + \frac{- 3}{x^{3}} \cdot \frac{5}{x^{6}}$

Step 1.13

Multiply $\frac{- 3}{x^{3}}$ by $\frac{5}{x^{6}}$ .

$\frac{8}{x^{9}} + \frac{- 3 \cdot 5}{x^{3} x^{6}}$

Step 1.14

Multiply $- 3$ by $5$ .

$\frac{8}{x^{9}} + \frac{- 15}{x^{3} x^{6}}$

Step 1.15

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

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Step 1.15.1

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

$\frac{8}{x^{9}} + \frac{- 15}{x^{3 + 6}}$

Step 1.15.2

Add $3$ and $6$ .

$\frac{8}{x^{9}} + \frac{- 15}{x^{9}}$

Step 1.16

Move the negative in front of the fraction.

$\frac{8}{x^{9}} - \frac{15}{x^{9}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{8 - 15}{x^{9}}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $15$ from $8$ .

$\frac{- 7}{x^{9}}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{7}{x^{9}}$