Solve (-10x^8)(-20x^80)

$$( - 10 x ^ { 8 } ) ( - 20 x ^ { 80 } )$$

Evaluate

$$200x^{88}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 80 to get 88.

$$-10x^{88}\left(-20\right)$$

Multiply -10 and -20 to get 200.

$$200x^{88}$$

Differentiate w.r.t. x

$$17600x^{87}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 80 to get 88.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{88}\left(-20\right))$$

Multiply -10 and -20 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(200x^{88})$$

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

$$88\times 200x^{88-1}$$

Multiply 88 times 200.

$$17600x^{88-1}$$

Subtract 1 from 88.

$$17600x^{87}$$