Solve frac{(qm^{0}p^2)^2}{3mp^3q^0}

$$\frac { ( q m ^ { 0 } p ^ { 2 } ) ^ { 2 } } { 3 m p ^ { 3 } q ^ { 0 } }$$

Evaluate

$$\frac{pq^{2}}{3m}$$

Solution Steps

Calculate m to the power of 0 and get 1.

$$\frac{\left(q\times 1p^{2}\right)^{2}}{3mp^{3}q^{0}}$$

Expand \left(q\times 1p^{2}\right)^{2}.

$$\frac{q^{2}\times 1^{2}\left(p^{2}\right)^{2}}{3mp^{3}q^{0}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{q^{2}\times 1^{2}p^{4}}{3mp^{3}q^{0}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{q^{2}\times 1p^{4}}{3mp^{3}q^{0}}$$

Calculate q to the power of 0 and get 1.

$$\frac{q^{2}\times 1p^{4}}{3mp^{3}\times 1}$$

Multiply 3 and 1 to get 3.

$$\frac{q^{2}\times 1p^{4}}{3mp^{3}}$$

Cancel out p^{3} in both numerator and denominator.

$$\frac{pq^{2}}{3m}$$

Differentiate w.r.t. q

$$\frac{2pq}{3m}$$