Simplify (r^-3s^5t^2)/(r^2st^-2)

$\frac{r^{- 3} s^{5} t^{2}}{r^{2} s t^{- 2}}$

Step 1

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

$\frac{s^{5} t^{2}}{r^{2} s t^{- 2} r^{3}}$

Step 2

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

Move $r^{3}$ .

$\frac{s^{5} t^{2}}{r^{3} r^{2} s t^{- 2}}$

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

$\frac{s^{5} t^{2}}{r^{3 + 2} s t^{- 2}}$

Add $3$ and $2$ .

$\frac{s^{5} t^{2}}{r^{5} s t^{- 2}}$

Step 3

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

$\frac{s^{5} t^{2} t^{2}}{r^{5} s}$

Step 4

Multiply $t^{2}$ by $t^{2}$ by adding the exponents.

Move $t^{2}$ .

$\frac{s^{5} (t^{2} t^{2})}{r^{5} s}$

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

$\frac{s^{5} t^{2 + 2}}{r^{5} s}$

Add $2$ and $2$ .

$\frac{s^{5} t^{4}}{r^{5} s}$

Step 5

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

Factor $s$ out of $s^{5} t^{4}$ .

$\frac{s (s^{4} t^{4})}{r^{5} s}$

Cancel the common factors.

Factor $s$ out of $r^{5} s$ .

$\frac{s (s^{4} t^{4})}{s r^{5}}$

Cancel the common factor.

$\frac{s (s^{4} t^{4})}{s r^{5}}$

Rewrite the expression.

$\frac{s^{4} t^{4}}{r^{5}}$