Solve yx^-1/(x^frac{5{4}x^0)^0}

$$\frac { y x ^ { - 1 } } { ( x ^ { \frac { 5 } { 4 } } x ^ { 0 } ) ^ { 0 } }$$

Evaluate

$$\frac{y}{x}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{4} and 0 to get \frac{5}{4}.

$$\frac{yx^{-1}}{\left(x^{\frac{5}{4}}\right)^{0}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{4} and 0 to get 0.

$$\frac{yx^{-1}}{x^{0}}$$

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

$$\frac{y}{x^{1}}$$

Calculate x to the power of 1 and get x.

$$\frac{y}{x}$$

Differentiate w.r.t. x

$$-\frac{y}{x^{2}}$$