Solve 4y^4x^-8/8x^-7y^-2

$$\frac { 4 y ^ { 4 } x ^ { - 8 } } { 8 x ^ { - 7 } y ^ { - 2 } }$$

Evaluate

$$\frac{y^{6}}{2x}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{x^{-8}y^{4}}{2x^{-7}y^{-2}}$$

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

$$\frac{x^{-8}y^{6}}{2x^{-7}}$$

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

$$\frac{y^{6}}{2x^{1}}$$

Calculate x to the power of 1 and get x.

$$\frac{y^{6}}{2x}$$

Differentiate w.r.t. x

$$-\frac{y^{6}}{2x^{2}}$$