Simplify (9x^5y^-3z^-2)/(3x^3y^3z^5)

$\frac{9 x^{5} y^{- 3} z^{- 2}}{3 x^{3} y^{3} z^{5}}$

Step 1

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

$\frac{9 x^{5} z^{- 2}}{3 x^{3} y^{3} z^{5} y^{3}}$

Step 2

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

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

Step 3

Simplify the denominator.

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

Move $y^{3}$ .

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

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

$\frac{9 x^{5}}{3 x^{3} y^{3 + 3} z^{5} z^{2}}$

Add $3$ and $3$ .

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

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

Move $z^{2}$ .

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

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

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

Add $2$ and $5$ .

$\frac{9 x^{5}}{3 x^{3} y^{6} z^{7}}$

Step 4

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 x^{5}$ .

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

Cancel the common factors.

Factor $3$ out of $3 x^{3} y^{6} z^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 x^{5}}{x^{3} y^{6} z^{7}}$

Step 5

Cancel the common factor of $x^{5}$ and $x^{3}$ .

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

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

Cancel the common factors.

Factor $x^{3}$ out of $x^{3} y^{6} z^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 x^{2}}{y^{6} z^{7}}$