Solve 1/a^6b^-3

$$\frac { 1 } { a ^ { 6 } b ^ { - 3 } }$$

Evaluate

$$\frac{b^{3}}{a^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{a^{6}b^{-3}}$$

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

$$\frac{1}{a^{6}}\times \frac{1}{b^{-3}}$$

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

$$a^{6\left(-1\right)}b^{-3\left(-1\right)}$$

Multiply 6 times -1.

$$\frac{1}{a^{6}}b^{-3\left(-1\right)}$$

Multiply -3 times -1.

$$\frac{1}{a^{6}}b^{3}$$

Differentiate w.r.t. a

$$-\frac{6b^{3}}{a^{7}}$$