Solve a^5*a^3*a^-2*a

$$a ^ { 5 } \cdot a ^ { 3 } \cdot a ^ { - 2 } \cdot a$$

Evaluate

$$a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$a^{8}a^{-2}a$$

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$a^{6}a$$

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

$$a^{7}$$

Differentiate w.r.t. a

$$7a^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8}a^{-2}a)$$

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

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

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

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

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

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

Subtract 1 from 7.

$$7a^{6}$$