Solve (7x^-7)(8x^2)

$$( 7 x ^ { - 7 } ) ( 8 x ^ { 2 } )$$

Evaluate

$$\frac{56}{x^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 2 to get -5.

$$7x^{-5}\times 8$$

Multiply 7 and 8 to get 56.

$$56x^{-5}$$

Differentiate w.r.t. x

$$-\frac{280}{x^{6}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -7 and 2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{-5}\times 8)$$

Multiply 7 and 8 to get 56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(56x^{-5})$$

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

$$-5\times 56x^{-5-1}$$

Multiply -5 times 56.

$$-280x^{-5-1}$$

Subtract 1 from -5.

$$-280x^{-6}$$