Solve (frac{X^{6}y^{7}z^{8}}{x^{-6}y^{8}z^4})x^2y^2z^2/xyz

$$( \frac { X ^ { 6 } y ^ { 7 } z ^ { 8 } } { x ^ { - 6 } y ^ { 8 } z ^ { 4 } } ) \frac { x ^ { 2 } y ^ { 2 } z ^ { 2 } } { x y z }$$

Evaluate

$$z^{5}X^{6}x^{7}$$

Solution Steps

Cancel out z^{4}y^{7} in both numerator and denominator.

$$\frac{z^{4}X^{6}}{x^{-6}y}\times \frac{x^{2}y^{2}z^{2}}{xyz}$$

Cancel out xyz in both numerator and denominator.

$$\frac{z^{4}X^{6}}{x^{-6}y}xyz$$

Express \frac{z^{4}X^{6}}{x^{-6}y}x as a single fraction.

$$\frac{z^{4}X^{6}x}{x^{-6}y}yz$$

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

$$\frac{z^{4}X^{6}x^{7}}{y}yz$$

Cancel out y and y.

$$z^{4}X^{6}x^{7}z$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$z^{5}X^{6}x^{7}$$

Differentiate w.r.t. x

$$7z^{5}\left(Xx\right)^{6}$$