Solve (32z^-4x^12)^-1

$$( 32 z ^ { - 4 } x ^ { 12 } ) ^ { - 1 }$$

Evaluate

$$\frac{z^{4}}{32x^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{32z^{-4}x^{12}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\frac{1}{32}\times \frac{1}{z^{-4}}\times \frac{1}{x^{12}}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{32}z^{-4\left(-1\right)}x^{12\left(-1\right)}$$

Multiply -4 times -1.

$$\frac{1}{32}z^{4}x^{12\left(-1\right)}$$

Multiply 12 times -1.

$$\frac{1}{32}z^{4}\times \frac{1}{x^{12}}$$

Differentiate w.r.t. x

$$-\frac{3z^{4}}{8x^{13}}$$