Solve frac{6a^{2}(a^-3)^6}{(a^-2)^-1}

$$\frac { 6 a ^ { 2 } ( a ^ { - 3 } ) ^ { 6 } } { ( a ^ { - 2 } ) ^ { - 1 } }$$

Evaluate

$$\frac{6}{a^{18}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 6 to get -18.

$$\frac{6a^{2}a^{-18}}{\left(a^{-2}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add 2 and -18 to get -16.

$$\frac{6a^{-16}}{\left(a^{-2}\right)^{-1}}$$

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

$$\frac{6a^{-16}}{a^{2}}$$

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

$$\frac{6}{a^{18}}$$

Differentiate w.r.t. a

$$-\frac{108}{a^{19}}$$