Algebra Examples

$(- \frac{5 y^{2}}{x^{6}}) (5 x^{4} y)$

Step 1

Cancel the common factor of $x^{4}$ .

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Step 1.1

Move the leading negative in $- \frac{5 y^{2}}{x^{6}}$ into the numerator.

$\frac{- 5 y^{2}}{x^{6}} (5 x^{4} y)$

Step 1.2

Factor $x^{4}$ out of $x^{6}$ .

$\frac{- 5 y^{2}}{x^{4} x^{2}} (5 x^{4} y)$

Step 1.3

Factor $x^{4}$ out of $5 x^{4} y$ .

$\frac{- 5 y^{2}}{x^{4} x^{2}} (x^{4} (5 y))$

Step 1.4

Cancel the common factor.

$\frac{- 5 y^{2}}{x^{4} x^{2}} (x^{4} (5 y))$

Step 1.5

Rewrite the expression.

$\frac{- 5 y^{2}}{x^{2}} (5 y)$

Step 2

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

$\frac{5 (- 5 y^{2})}{x^{2}} y$

Step 3

Multiply $- 5$ by $5$ .

$\frac{- 25 y^{2}}{x^{2}} y$

Step 4

Combine $\frac{- 25 y^{2}}{x^{2}}$ and $y$ .

$\frac{- 25 y^{2} y}{x^{2}}$

Step 5

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

$\frac{- 25 (y^{1} y^{2})}{x^{2}}$

Step 6

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

$\frac{- 25 y^{1 + 2}}{x^{2}}$

Step 7

Add $1$ and $2$ .

$\frac{- 25 y^{3}}{x^{2}}$

Step 8

Move the negative in front of the fraction.

$- \frac{25 y^{3}}{x^{2}}$