Solve (5a^-4)(3a^-2)

$$( 5 a ^ { - 4 } ) ( 3 a ^ { - 2 } )$$

Evaluate

$$\frac{15}{a^{6}}$$

Solution Steps

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

$$5a^{-6}\times 3$$

Multiply 5 and 3 to get 15.

$$15a^{-6}$$

Differentiate w.r.t. a

$$-\frac{90}{a^{7}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a^{-6}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(15a^{-6})$$

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

$$-6\times 15a^{-6-1}$$

Multiply -6 times 15.

$$-90a^{-6-1}$$

Subtract 1 from -6.

$$-90a^{-7}$$