Solve (32p^5q^20)^frac{3{5}}

$$( 32 p ^ { 5 } q ^ { 20 } ) ^ { \frac { 3 } { 5 } }$$

Evaluate

$$8p^{3}q^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(32p^{5}q^{20}\right)^{\frac{3}{5}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$32^{\frac{3}{5}}\left(p^{5}\right)^{\frac{3}{5}}\left(q^{20}\right)^{\frac{3}{5}}$$

Raise 32 to the power \frac{3}{5}.

$$8\left(p^{5}\right)^{\frac{3}{5}}\left(q^{20}\right)^{\frac{3}{5}}$$

To raise a power to another power, multiply the exponents.

$$8p^{5\times \frac{3}{5}}q^{20\times \frac{3}{5}}$$

Multiply 5 times \frac{3}{5}.

$$8p^{3}q^{20\times \frac{3}{5}}$$

Multiply 20 times \frac{3}{5}.

$$8p^{3}q^{12}$$

Differentiate w.r.t. p

$$24p^{2}q^{12}$$