Simplify (6x^2)/(y^3)*(y^-2x^3)/(9x^2)

$\frac{6 x^{2}}{y^{3}} \cdot \frac{y^{- 2} x^{3}}{9 x^{2}}$

Step 1

Combine.

$\frac{6 x^{2} (y^{- 2} x^{3})}{y^{3} (9 x^{2})}$

Step 2

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

Move $x^{3}$ .

$\frac{6 (x^{3} x^{2}) y^{- 2}}{y^{3} (9 x^{2})}$

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

$\frac{6 x^{3 + 2} y^{- 2}}{y^{3} (9 x^{2})}$

Add $3$ and $2$ .

$\frac{6 x^{5} y^{- 2}}{y^{3} (9 x^{2})}$

Step 3

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

$\frac{6 x^{5}}{y^{3} (9 x^{2}) y^{2}}$

Step 4

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

Move $y^{2}$ .

$\frac{6 x^{5}}{y^{2} y^{3} (9 x^{2})}$

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

$\frac{6 x^{5}}{y^{2 + 3} (9 x^{2})}$

Add $2$ and $3$ .

$\frac{6 x^{5}}{y^{5} (9 x^{2})}$

Step 5

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6 x^{5}$ .

$\frac{3 (2 x^{5})}{y^{5} (9 x^{2})}$

Cancel the common factors.

Factor $3$ out of $y^{5} (9 x^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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

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

Cancel the common factors.

Factor $x^{2}$ out of $y^{5} (3 x^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Move $3$ to the left of $y^{5}$ .

$\frac{2 x^{3}}{3 y^{5}}$

Simplify (6x^2)/(y^3)*(y^-2x^3)/(9x^2)

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