Solve (a^2)^3*a^4

$$( a ^ { 2 } ) ^ { 3 } \times a ^ { 4 }$$

Evaluate

$$a^{10}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$a^{6}a^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$a^{10}$$

Differentiate w.r.t. a

$$10a^{9}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}a^{4})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

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

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

$$10a^{10-1}$$

Subtract 1 from 10.

$$10a^{9}$$