Algebra Examples

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

Step 1

Multiply $x$ by $x^{5}$ by adding the exponents.

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Step 1.1

Multiply $x$ by $x^{5}$ .

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Step 1.1.1

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

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

Step 1.1.2

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

$\frac{x^{1 + 5} y^{- 2}}{y^{- 8}}$

Step 1.2

Add $1$ and $5$ .

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

Step 2

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{6} y^{- 2} y^{8}$

Step 3

Multiply $y^{- 2}$ by $y^{8}$ by adding the exponents.

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Step 3.1

Move $y^{8}$ .

$x^{6} (y^{8} y^{- 2})$

Step 3.2

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

$x^{6} y^{8 - 2}$

Step 3.3

Subtract $2$ from $8$ .

$x^{6} y^{6}$