Simplify (15w^-3x^5y^2)/(6w^-2x^-2y)

$\frac{15 w^{- 3} x^{5} y^{2}}{6 w^{- 2} x^{- 2} y}$

Step 1

Move $w^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{15 x^{5} y^{2}}{6 w^{- 2} x^{- 2} y w^{3}}$

Step 2

Simplify the denominator.

Multiply $w^{- 2}$ by $w^{3}$ by adding the exponents.

Move $w^{3}$ .

$\frac{15 x^{5} y^{2}}{6 (w^{3} w^{- 2}) x^{- 2} y}$

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

$\frac{15 x^{5} y^{2}}{6 w^{3 - 2} x^{- 2} y}$

Subtract $2$ from $3$ .

$\frac{15 x^{5} y^{2}}{6 w^{1} x^{- 2} y}$

Simplify $6 w^{1} x^{- 2} y$ .

$\frac{15 x^{5} y^{2}}{6 w x^{- 2} y}$

Step 3

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 x^{5} y^{2} x^{2}}{6 w y}$

Step 4

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{15 (x^{2} x^{5}) y^{2}}{6 w y}$

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

$\frac{15 x^{2 + 5} y^{2}}{6 w y}$

Add $2$ and $5$ .

$\frac{15 x^{7} y^{2}}{6 w y}$

Step 5

Cancel the common factor of $15$ and $6$ .

Factor $3$ out of $15 x^{7} y^{2}$ .

$\frac{3 (5 x^{7} y^{2})}{6 w y}$

Cancel the common factors.

Factor $3$ out of $6 w y$ .

$\frac{3 (5 x^{7} y^{2})}{3 (2 w y)}$

Cancel the common factor.

$\frac{3 (5 x^{7} y^{2})}{3 (2 w y)}$

Rewrite the expression.

$\frac{5 x^{7} y^{2}}{2 w y}$

Step 6

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

Factor $y$ out of $5 x^{7} y^{2}$ .

$\frac{y (5 x^{7} y)}{2 w y}$

Cancel the common factors.

Factor $y$ out of $2 w y$ .

$\frac{y (5 x^{7} y)}{y (2 w)}$

Cancel the common factor.

$\frac{y (5 x^{7} y)}{y (2 w)}$

Rewrite the expression.

$\frac{5 x^{7} y}{2 w}$

Simplify (15w^-3x^5y^2)/(6w^-2x^-2y)

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