Solve frac{3a^{-2}b*24b^-1a^-1}{9a^-4b^-3}

$$\frac { 3 a ^ { - 2 } b \times 24 b ^ { - 1 } a ^ { - 1 } } { 9 a ^ { - 4 } b ^ { - 3 } }$$

Evaluate

$$8ab^{3}$$

Solution Steps

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

$$\frac{3a^{-3}b\times 24b^{-1}}{9a^{-4}b^{-3}}$$

Multiply b and b^{-1} to get 1.

$$\frac{3a^{-3}\times 24}{9a^{-4}b^{-3}}$$

Cancel out 3\times 3 in both numerator and denominator.

$$\frac{8a^{-3}}{a^{-4}b^{-3}}$$

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

$$\frac{8a^{1}}{b^{-3}}$$

Calculate a to the power of 1 and get a.

$$\frac{8a}{b^{-3}}$$

Differentiate w.r.t. b

$$24ab^{2}$$