Solve frac{a^{-2}b^2}{b^-3}:ab^4/a^4

$$\frac { a ^ { - 2 } b ^ { 2 } } { b ^ { - 3 } } : \frac { a b ^ { 4 } } { a ^ { 4 } }$$

Evaluate

$$ab$$

Solution Steps

Divide \frac{a^{-2}b^{2}}{b^{-3}} by \frac{ab^{4}}{a^{4}} by multiplying \frac{a^{-2}b^{2}}{b^{-3}} by the reciprocal of \frac{ab^{4}}{a^{4}}.

$$\frac{a^{-2}b^{2}a^{4}}{b^{-3}ab^{4}}$$

Cancel out ab^{2} in both numerator and denominator.

$$\frac{a^{-2}a^{3}}{b^{-3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{a^{1}}{b^{-3}b^{2}}$$

Calculate a to the power of 1 and get a.

$$\frac{a}{b^{-3}b^{2}}$$

To multiply powers of the same base, add their exponents. Add -3 and 2 to get -1.

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

Differentiate w.r.t. b

$$a$$