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

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

Evaluate

$$a^{3}$$

Solution Steps

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

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

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

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

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

$$a^{1}a^{2}a^{0}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$a^{3}a^{0}$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$a^{3}$$

Differentiate w.r.t. a

$$3a^{2}$$

Steps Using Definition of a Derivative

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{1}a^{2}a^{0})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}a^{0})$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3})$$

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

$$3a^{3-1}$$

Subtract 1 from 3.

$$3a^{2}$$