Solve frac{a^{-5}b^{3}}{a^{-1}b^{4}}*a^2b^4/a^-3b^-1

$$\frac { a ^ { - 5 } b ^ { 3 } } { a ^ { - 1 } b ^ { 4 } } \times \frac { a ^ { 2 } b ^ { 4 } } { a ^ { - 3 } b ^ { - 1 } }$$

Evaluate

$$ab^{4}$$

Solution Steps

Cancel out b^{3} in both numerator and denominator.

$$\frac{a^{-5}}{\frac{1}{a}b}\times \frac{a^{2}b^{4}}{a^{-3}b^{-1}}$$

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

$$\frac{1}{ba^{4}}\times \frac{a^{2}b^{4}}{a^{-3}b^{-1}}$$

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

$$\frac{1}{ba^{4}}a^{5}b^{5}$$

Express \frac{1}{ba^{4}}a^{5} as a single fraction.

$$\frac{a^{5}}{ba^{4}}b^{5}$$

Cancel out a^{4} in both numerator and denominator.

$$\frac{a}{b}b^{5}$$

Express \frac{a}{b}b^{5} as a single fraction.

$$\frac{ab^{5}}{b}$$

Cancel out b in both numerator and denominator.

$$ab^{4}$$

Differentiate w.r.t. b

$$4ab^{3}$$