Solve frac{5^{2}y^-10}{5^-1z^0x^-5}

$$\frac { 5 ^ { 2 } y ^ { - 10 } } { 5 ^ { - 1 } z ^ { 0 } x ^ { - 5 } }$$

Evaluate

$$\frac{125x^{5}}{y^{10}}$$

Short Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{5^{3}y^{-10}}{x^{-5}z^{0}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125y^{-10}}{x^{-5}z^{0}}$$

Calculate z to the power of 0 and get 1.

$$\frac{125y^{-10}}{x^{-5}\times 1}$$

Cancel out 1 in both numerator and denominator.

$$\frac{125y^{-10}}{x^{-5}}$$

Differentiate w.r.t. x

$$\frac{625x^{4}}{y^{10}}$$