Solve left(a^4right)^1left(a^2right)^1{left({a}^3right)}^0

$${ \left( { a }^{ 4 } \right) }^{ 1 } { \left( { a }^{ 2 } \right) }^{ 1 } { \left( { a }^{ 3 } \right) }^{ 0 }$$

Evaluate

$$a^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 1 to get 4.

$$a^{4}\left(a^{2}\right)^{1}\left(a^{3}\right)^{0}$$

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

$$a^{4}a^{2}\left(a^{3}\right)^{0}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$a^{4}a^{2}a^{0}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$a^{6}a^{0}$$

To multiply powers of the same base, add their exponents. Add 6 and 0 to get 6.

$$a^{6}$$

Differentiate w.r.t. a

$$6a^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}\left(a^{2}\right)^{1}\left(a^{3}\right)^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{2}\left(a^{3}\right)^{0})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{2}a^{0})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}a^{0})$$

To multiply powers of the same base, add their exponents. Add 6 and 0 to get 6.

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

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

$$6a^{6-1}$$

Subtract 1 from 6.

$$6a^{5}$$