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

$$( - a ) \cdot ( a ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-a^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

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

$$-1^{3}a^{1}a^{2\times 3}$$

Multiply 2 times 3.

$$-1^{3}a^{1}a^{6}$$

To multiply powers of the same base, add their exponents.

$$-1^{3}a^{1+6}$$

Add the exponents 1 and 6.

$$-1^{3}a^{7}$$

Differentiate w.r.t. a

$$-7a^{6}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{7})$$

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

$$7\left(-1\right)a^{7-1}$$

Multiply 7 times -1.

$$-7a^{7-1}$$

Subtract 1 from 7.

$$-7a^{6}$$