Solve (36p^2q^6)^-frac{1{2}}

$$( 36 p ^ { 2 } q ^ { 6 } ) ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{1}{6|p|\left(|q|\right)^{3}}$$

Solution Steps

Expand \left(36p^{2}q^{6}\right)^{-\frac{1}{2}}.

$$36^{-\frac{1}{2}}\left(p^{2}\right)^{-\frac{1}{2}}\left(q^{6}\right)^{-\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -\frac{1}{2} to get -1.

$$36^{-\frac{1}{2}}p^{-1}\left(q^{6}\right)^{-\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -\frac{1}{2} to get -3.

$$36^{-\frac{1}{2}}p^{-1}q^{-3}$$

Calculate 36 to the power of -\frac{1}{2} and get \frac{1}{6}.

$$\frac{1}{6}p^{-1}q^{-3}$$

Differentiate w.r.t. q

$$-\frac{|q|}{2|p|q^{5}}$$