Solve frac{p^{0}q}{p^-8q^-1*p^0q^0}

$$\frac { p ^ { 0 } q } { p ^ { - 8 } q ^ { - 1 } \cdot p ^ { 0 } q ^ { 0 } }$$

Evaluate

$$q^{2}p^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and 0 to get -8.

$$\frac{p^{0}q}{p^{-8}q^{-1}q^{0}}$$

To multiply powers of the same base, add their exponents. Add -1 and 0 to get -1.

$$\frac{p^{0}q}{p^{-8}q^{-1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$q^{2}p^{8}$$

Differentiate w.r.t. p

$$8q^{2}p^{7}$$