Solve a^{2}b^-3div(a^4b^2)^-1

$$a ^ { 2 } b ^ { - 3 } \div ( a ^ { 4 } b ^ { 2 } ) ^ { - 1 }$$

Evaluate

$$\frac{a^{6}}{b}$$

Solution Steps

Expand \left(a^{4}b^{2}\right)^{-1}.

$$\frac{a^{2}b^{-3}}{\left(a^{4}\right)^{-1}\left(b^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -1 to get -4.

$$\frac{a^{2}b^{-3}}{a^{-4}\left(b^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

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

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

$$\frac{b^{-3}a^{6}}{b^{-2}}$$

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

$$\frac{a^{6}}{b^{1}}$$

Calculate b to the power of 1 and get b.

$$\frac{a^{6}}{b}$$

Differentiate w.r.t. a

$$\frac{6a^{5}}{b}$$