Solve (frac{x^{9}y^{2}z^5}{x^4yz^2})^-1

$$( \frac { x ^ { 9 } y ^ { 2 } z ^ { 5 } } { x ^ { 4 } y z ^ { 2 } } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{yz^{3}x^{5}}$$

Solution Steps

Cancel out yz^{2}x^{4} in both numerator and denominator.

$$\left(yz^{3}x^{5}\right)^{-1}$$

Expand \left(yz^{3}x^{5}\right)^{-1}.

$$y^{-1}\left(z^{3}\right)^{-1}\left(x^{5}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$y^{-1}z^{-3}\left(x^{5}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -1 to get -5.

$$y^{-1}z^{-3}x^{-5}$$

Differentiate w.r.t. x

$$-\frac{5}{yz^{3}x^{6}}$$