Solve x^0z^2.5/27frac{2{3}y^-2z^0.5}

$$\frac{ { x }^{ 0 } { z }^{ 2.5 } }{ 27 \frac{ 2 }{ 3 } { y }^{ -2 } { z }^{ 0.5 } }$$

Evaluate

$$\frac{3\left(yz\right)^{2}}{83}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{1z^{2.5}}{\frac{27\times 3+2}{3}y^{-2}z^{0.5}}$$

Multiply 27 and 3 to get 81.

$$\frac{1z^{2.5}}{\frac{81+2}{3}y^{-2}z^{0.5}}$$

Add 81 and 2 to get 83.

$$\frac{1z^{2.5}}{\frac{83}{3}y^{-2}z^{0.5}}$$

Cancel out \sqrt{z} in both numerator and denominator.

$$\frac{z^{2}}{\frac{83}{3}y^{-2}}$$

Differentiate w.r.t. y

$$\frac{6yz^{2}}{83}$$