Solve frac{p^{0}q^9}{p^0q*p^9q^-6}

$$\frac { p ^ { 0 } q ^ { 9 } } { p ^ { 0 } q \cdot p ^ { 9 } q ^ { - 6 } }$$

Evaluate

$$\frac{q^{14}}{p^{9}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and 9 to get 9.

$$\frac{p^{0}q^{9}}{p^{9}qq^{-6}}$$

To multiply powers of the same base, add their exponents. Add 1 and -6 to get -5.

$$\frac{p^{0}q^{9}}{p^{9}q^{-5}}$$

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

$$\frac{p^{0}q^{14}}{p^{9}}$$

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

$$\frac{q^{14}}{p^{9}}$$

Differentiate w.r.t. p

$$-\frac{9q^{14}}{p^{10}}$$