Solve (a^2)^-4*a^-2/a^-12=

$$\frac { ( a ^ { 2 } ) ^ { - 4 } \cdot a ^ { - 2 } } { a ^ { - 12 } } =$$

Evaluate

$$a^{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{a^{-8}a^{-2}}{a^{-12}}$$

To multiply powers of the same base, add their exponents. Add -8 and -2 to get -10.

$$\frac{a^{-10}}{a^{-12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -12 from -10 to get 2.

$$a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-8}a^{-2}}{a^{-12}})$$

To multiply powers of the same base, add their exponents. Add -8 and -2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{-10}}{a^{-12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -12 from -10 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2a^{2-1}$$

Subtract 1 from 2.

$$2a^{1}$$

For any term t, t^{1}=t.

$$2a$$