Solve 1/a^14b^-10

$$\frac { 1 } { a ^ { 14 } b ^ { - 10 } }$$

Evaluate

$$\frac{b^{10}}{a^{14}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{a^{14}b^{-10}}$$

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

$$\frac{1}{a^{14}}\times \frac{1}{b^{-10}}$$

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

$$a^{14\left(-1\right)}b^{-10\left(-1\right)}$$

Multiply 14 times -1.

$$\frac{1}{a^{14}}b^{-10\left(-1\right)}$$

Multiply -10 times -1.

$$\frac{1}{a^{14}}b^{10}$$

Differentiate w.r.t. a

$$-\frac{14b^{10}}{a^{15}}$$