Simplify (p^3q^(5/2))/(q^2r^-6)

$\frac{p^{3} q^{\frac{5}{2}}}{q^{2} r^{- 6}}$

Step 1

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

$\frac{p^{3} q^{\frac{5}{2}} q^{- 2}}{r^{- 6}}$

Step 2

Move $r^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$p^{3} q^{\frac{5}{2}} q^{- 2} r^{6}$

Step 3

Multiply $q^{\frac{5}{2}}$ by $q^{- 2}$ by adding the exponents.

Move $q^{- 2}$ .

$p^{3} (q^{- 2} q^{\frac{5}{2}}) r^{6}$

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

$p^{3} q^{- 2 + \frac{5}{2}} r^{6}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$p^{3} q^{- 2 \cdot \frac{2}{2} + \frac{5}{2}} r^{6}$

Combine $- 2$ and $\frac{2}{2}$ .

$p^{3} q^{\frac{- 2 \cdot 2}{2} + \frac{5}{2}} r^{6}$

Combine the numerators over the common denominator.

$p^{3} q^{\frac{- 2 \cdot 2 + 5}{2}} r^{6}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$p^{3} q^{\frac{- 4 + 5}{2}} r^{6}$

Add $- 4$ and $5$ .

$p^{3} q^{\frac{1}{2}} r^{6}$

Step 4

Reorder factors in $p^{3} q^{\frac{1}{2}} r^{6}$ .

$p^{3} r^{6} q^{\frac{1}{2}}$