Simplify (9p^3q^2rs^0t^-1)/(3p^2r^2t)

$\frac{9 p^{3} q^{2} r s^{0} t^{- 1}}{3 p^{2} r^{2} t}$

Step 1

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

$\frac{9 p^{3} q^{2} r}{3 p^{2} r^{2} t \cdot t}$

Step 2

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$\frac{9 p^{3} q^{2} r}{3 p^{2} r^{2} (t \cdot t)}$

Multiply $t$ by $t$ .

$\frac{9 p^{3} q^{2} r}{3 p^{2} r^{2} t^{2}}$

Step 3

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

Factor $3$ out of $9 p^{3} q^{2} r$ .

$\frac{3 (3 p^{3} q^{2} r)}{3 p^{2} r^{2} t^{2}}$

Cancel the common factors.

Factor $3$ out of $3 p^{2} r^{2} t^{2}$ .

$\frac{3 (3 p^{3} q^{2} r)}{3 (p^{2} r^{2} t^{2})}$

Cancel the common factor.

$\frac{3 (3 p^{3} q^{2} r)}{3 (p^{2} r^{2} t^{2})}$

Rewrite the expression.

$\frac{3 p^{3} q^{2} r}{p^{2} r^{2} t^{2}}$

Step 4

Cancel the common factor of $p^{3}$ and $p^{2}$ .

Factor $p^{2}$ out of $3 p^{3} q^{2} r$ .

$\frac{p^{2} (3 p q^{2} r)}{p^{2} r^{2} t^{2}}$

Cancel the common factors.

Factor $p^{2}$ out of $p^{2} r^{2} t^{2}$ .

$\frac{p^{2} (3 p q^{2} r)}{p^{2} (r^{2} t^{2})}$

Cancel the common factor.

$\frac{p^{2} (3 p q^{2} r)}{p^{2} (r^{2} t^{2})}$

Rewrite the expression.

$\frac{3 p q^{2} r}{r^{2} t^{2}}$

Step 5

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

Factor $r$ out of $3 p q^{2} r$ .

$\frac{r (3 p q^{2})}{r^{2} t^{2}}$

Cancel the common factors.

Factor $r$ out of $r^{2} t^{2}$ .

$\frac{r (3 p q^{2})}{r (r t^{2})}$

Cancel the common factor.

$\frac{r (3 p q^{2})}{r (r t^{2})}$

Rewrite the expression.

$\frac{3 p q^{2}}{r t^{2}}$