Solve (8p^3/2q^5/2)^2/3

$$( 8 p ^ { 3 / 2 } q ^ { 5 / 2 } ) ^ { 2 / 3 }$$

Evaluate

$$4pq^{\frac{5}{3}}$$

Solution Steps

Expand \left(8p^{\frac{3}{2}}q^{\frac{5}{2}}\right)^{\frac{2}{3}}.

$$8^{\frac{2}{3}}\left(p^{\frac{3}{2}}\right)^{\frac{2}{3}}\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}$$

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

$$8^{\frac{2}{3}}p^{1}\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{2} and \frac{2}{3} to get \frac{5}{3}.

$$8^{\frac{2}{3}}p^{1}q^{\frac{5}{3}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$4p^{1}q^{\frac{5}{3}}$$

Calculate p to the power of 1 and get p.

$$4pq^{\frac{5}{3}}$$

Differentiate w.r.t. p

$$4q^{\frac{5}{3}}$$