Algebra Examples

$\frac{x^{- 7}}{8 y^{2}} \cdot \frac{8}{x^{8} y^{- 2}}$

Step 1

Combine.

$\frac{x^{- 7} \cdot 8}{8 y^{2} (x^{8} y^{- 2})}$

Step 2

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

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Step 2.1

Move $y^{- 2}$ .

$\frac{x^{- 7} \cdot 8}{8 (y^{- 2} y^{2}) x^{8}}$

Step 2.2

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

$\frac{x^{- 7} \cdot 8}{8 y^{- 2 + 2} x^{8}}$

Step 2.3

Add $- 2$ and $2$ .

$\frac{x^{- 7} \cdot 8}{8 y^{0} x^{8}}$

Step 3

Simplify $8 y^{0} x^{8}$ .

$\frac{x^{- 7} \cdot 8}{8 x^{8}}$

Step 4

Move $x^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{8}{8 x^{8} x^{7}}$

Step 5

Multiply $x^{8}$ by $x^{7}$ by adding the exponents.

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Step 5.1

Move $x^{7}$ .

$\frac{8}{8 (x^{7} x^{8})}$

Step 5.2

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

$\frac{8}{8 x^{7 + 8}}$

Step 5.3

Add $7$ and $8$ .

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

Step 6

Cancel the common factor of $8$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{x^{15}}$