Solve [(a^4)^2]^-3

$$[ ( a ^ { 4 } ) ^ { 2 } ] ^ { - 3 }$$

Evaluate

$$\frac{1}{a^{24}}$$

Steps for Raising Power to Another Power

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

$$\left(a^{8}\right)^{-3}$$

To raise a power to another power, multiply the exponents.

$$a^{8\left(-3\right)}$$

Multiply 8 times -3.

$$\frac{1}{a^{24}}$$

Differentiate w.r.t. a

$$-\frac{24}{a^{25}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(a^{8}\right)^{-3})$$

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{-24})$$

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

$$-24a^{-24-1}$$

Subtract 1 from -24.

$$-24a^{-25}$$