Solve (-3*x^5/x^2*w^4)^-1

$$( \frac { - 3 \cdot x ^ { 5 } } { x ^ { 2 } \cdot w ^ { 4 } } ) ^ { - 1 }$$

Evaluate

$$-\frac{w^{4}}{3x^{3}}$$

Solution Steps

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

$$\left(\frac{-3x^{3}}{w^{4}}\right)^{-1}$$

To raise \frac{-3x^{3}}{w^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3x^{3}\right)^{-1}}{\left(w^{4}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -1 to get -4.

$$\frac{\left(-3x^{3}\right)^{-1}}{w^{-4}}$$

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

$$\frac{\left(-3\right)^{-1}\left(x^{3}\right)^{-1}}{w^{-4}}$$

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

$$\frac{\left(-3\right)^{-1}x^{-3}}{w^{-4}}$$

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$\frac{-\frac{1}{3}x^{-3}}{w^{-4}}$$

Differentiate w.r.t. x

$$\left(\frac{w}{x}\right)^{4}$$