Solve (a^18/b^18)(b^-20/a^20)

$$( \frac { a ^ { 18 } } { b ^ { 18 } } ) ( \frac { b ^ { - 20 } } { a ^ { 20 } } )$$

Evaluate

$$\frac{1}{a^{2}b^{38}}$$

Solution Steps

Multiply \frac{a^{18}}{b^{18}} times \frac{b^{-20}}{a^{20}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{18}b^{-20}}{b^{18}a^{20}}$$

Cancel out a^{18} in both numerator and denominator.

$$\frac{b^{-20}}{a^{2}b^{18}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{a^{2}b^{38}}$$

Differentiate w.r.t. b

$$-\frac{38}{a^{2}b^{39}}$$