Solve frac{(-3x^{-4}y)^-4}{(5x^-2y^3)^0}

$$\frac { ( - 3 x ^ { - 4 } y ) ^ { - 4 } } { ( 5 x ^ { - 2 } y ^ { 3 } ) ^ { 0 } }$$

Evaluate

$$\frac{x^{16}}{81y^{4}}$$

Solution Steps

Expand \left(-3x^{-4}y\right)^{-4}.

$$\frac{\left(-3\right)^{-4}\left(x^{-4}\right)^{-4}y^{-4}}{\left(5x^{-2}y^{3}\right)^{0}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -4 to get 16.

$$\frac{\left(-3\right)^{-4}x^{16}y^{-4}}{\left(5x^{-2}y^{3}\right)^{0}}$$

Calculate -3 to the power of -4 and get \frac{1}{81}.

$$\frac{\frac{1}{81}x^{16}y^{-4}}{\left(5x^{-2}y^{3}\right)^{0}}$$

Calculate 5x^{-2}y^{3} to the power of 0 and get 1.

$$\frac{\frac{1}{81}x^{16}y^{-4}}{1}$$

Anything divided by one gives itself.

$$\frac{1}{81}x^{16}y^{-4}$$

Differentiate w.r.t. x

$$\frac{16x^{15}}{81y^{4}}$$