Solve (2a^6b^-4)^-1

$$( 2 a ^ { 6 } b ^ { - 4 } ) ^ { - 1 }$$

Evaluate

$$\frac{b^{4}}{2a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{2a^{6}b^{-4}}$$

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

$$\frac{1}{2}\times \frac{1}{a^{6}}\times \frac{1}{b^{-4}}$$

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

$$\frac{1}{2}a^{6\left(-1\right)}b^{-4\left(-1\right)}$$

Multiply 6 times -1.

$$\frac{1}{2}\times \frac{1}{a^{6}}b^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$\frac{1}{2}\times \frac{1}{a^{6}}b^{4}$$

Differentiate w.r.t. a

$$-\frac{3b^{4}}{a^{7}}$$