Simplify (9x^3y^-10z^6)/(3xy^2z^-3)

$\frac{9 x^{3} y^{- 10} z^{6}}{3 x y^{2} z^{- 3}}$

Step 1

Move $y^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{9 x^{3} z^{6}}{3 x y^{2} z^{- 3} y^{10}}$

Step 2

Multiply $y^{2}$ by $y^{10}$ by adding the exponents.

Move $y^{10}$ .

$\frac{9 x^{3} z^{6}}{3 x (y^{10} y^{2}) z^{- 3}}$

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

$\frac{9 x^{3} z^{6}}{3 x y^{10 + 2} z^{- 3}}$

Add $10$ and $2$ .

$\frac{9 x^{3} z^{6}}{3 x y^{12} z^{- 3}}$

Step 3

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

$\frac{9 x^{3} z^{6} z^{3}}{3 x y^{12}}$

Step 4

Multiply $z^{6}$ by $z^{3}$ by adding the exponents.

Move $z^{3}$ .

$\frac{9 x^{3} (z^{3} z^{6})}{3 x y^{12}}$

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

$\frac{9 x^{3} z^{3 + 6}}{3 x y^{12}}$

Add $3$ and $6$ .

$\frac{9 x^{3} z^{9}}{3 x y^{12}}$

Step 5

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

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

$\frac{3 (3 x^{3} z^{9})}{3 x y^{12}}$

Cancel the common factors.

Factor $3$ out of $3 x y^{12}$ .

$\frac{3 (3 x^{3} z^{9})}{3 (x y^{12})}$

Cancel the common factor.

$\frac{3 (3 x^{3} z^{9})}{3 (x y^{12})}$

Rewrite the expression.

$\frac{3 x^{3} z^{9}}{x y^{12}}$

Step 6

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

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

$\frac{x (3 x^{2} z^{9})}{x y^{12}}$

Cancel the common factors.

Factor $x$ out of $x y^{12}$ .

$\frac{x (3 x^{2} z^{9})}{x (y^{12})}$

Cancel the common factor.

$\frac{x (3 x^{2} z^{9})}{x y^{12}}$

Rewrite the expression.

$\frac{3 x^{2} z^{9}}{y^{12}}$