Solve (a^4)^7*(a^2)^11quad6114

$$( a ^ { 4 } ) ^ { 7 } \cdot ( a ^ { 2 } ) ^ { 11 } \quad 6114$$

Evaluate

$$6114a^{50}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 7 to get 28.

$$a^{28}\left(a^{2}\right)^{11}\times 6114$$

To raise a power to another power, multiply the exponents. Multiply 2 and 11 to get 22.

$$a^{28}a^{22}\times 6114$$

To multiply powers of the same base, add their exponents. Add 28 and 22 to get 50.

$$a^{50}\times 6114$$

Differentiate w.r.t. a

$$305700a^{49}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 7 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{28}\left(a^{2}\right)^{11}\times 6114)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 11 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{28}a^{22}\times 6114)$$

To multiply powers of the same base, add their exponents. Add 28 and 22 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{50}\times 6114)$$

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

$$50\times 6114a^{50-1}$$

Multiply 50 times 6114.

$$305700a^{50-1}$$

Subtract 1 from 50.

$$305700a^{49}$$