Algebra Examples

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

Step 1

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

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Step 1.1

Move the leading negative in $- \frac{4 x^{4}}{y^{4}}$ into the numerator.

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

Step 1.2

Factor $y^{2}$ out of $y^{4}$ .

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

Step 1.3

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

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

Step 1.4

Cancel the common factor.

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

Step 1.5

Rewrite the expression.

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

Step 2

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

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

Step 3

Multiply $- 4$ by $2$ .

$\frac{- 8 x^{4}}{y^{2}} x^{3}$

Step 4

Combine $\frac{- 8 x^{4}}{y^{2}}$ and $x^{3}$ .

$\frac{- 8 x^{4} x^{3}}{y^{2}}$

Step 5

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Step 5.1

Move $x^{3}$ .

$\frac{- 8 (x^{3} x^{4})}{y^{2}}$

Step 5.2

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

$\frac{- 8 x^{3 + 4}}{y^{2}}$

Step 5.3

Add $3$ and $4$ .

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

Step 6

Move the negative in front of the fraction.

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