Solve q^{-1}r^{-1}*q^5r^6*q^-1r^0

$$q ^ { - 1 } r ^ { - 1 } \cdot q ^ { 5 } r ^ { 6 } \cdot q ^ { - 1 } r ^ { 0 }$$

Evaluate

$$q^{3}r^{5}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\frac{1}{q}\times \frac{1}{r}q^{5}r^{6}r^{0}\times \frac{1}{q}$$

Use the Commutative Property of Multiplication.

$$\frac{1}{q}r^{6}\times \frac{1}{r}r^{0}q^{5}\times \frac{1}{q}$$

To multiply powers of the same base, add their exponents.

$$\frac{1}{q}r^{6}\times \frac{1}{r}q^{5-1}$$

Add the exponents 5 and -1.

$$\frac{1}{q}r^{6}\times \frac{1}{r}q^{4}$$

Multiply \frac{1}{q} times r^{6}.

$$\frac{r^{6}}{q}\times \frac{1}{r}q^{4}$$

Differentiate w.r.t. q

$$3q^{2}r^{5}$$