Solve (z^2*5)^3/sqrt{4}

$$\frac { ( z ^ { 2 } \times 5 ) ^ { 3 } } { \sqrt { 4 } }$$

Evaluate

$$\frac{125z^{6}}{2}$$

Solution Steps

Expand \left(z^{2}\times 5\right)^{3}.

$$\frac{\left(z^{2}\right)^{3}\times 5^{3}}{\sqrt{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{z^{6}\times 5^{3}}{\sqrt{4}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{z^{6}\times 125}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{z^{6}\times 125}{2}$$

Differentiate w.r.t. z

$$375z^{5}$$