Solve (8x^6)(-7x^6)(8x^4)

$$( 8 x ^ { 6 } ) ( - 7 x ^ { 6 } ) ( 8 x ^ { 4 } )$$

Evaluate

$$-448x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$8x^{12}\left(-7\right)\times 8x^{4}$$

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

$$8x^{16}\left(-7\right)\times 8$$

Multiply 8 and -7 to get -56.

$$-56x^{16}\times 8$$

Multiply -56 and 8 to get -448.

$$-448x^{16}$$

Differentiate w.r.t. x

$$-7168x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{12}\left(-7\right)\times 8x^{4})$$

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{16}\left(-7\right)\times 8)$$

Multiply 8 and -7 to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-56x^{16}\times 8)$$

Multiply -56 and 8 to get -448.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-448x^{16})$$

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

$$16\left(-448\right)x^{16-1}$$

Multiply 16 times -448.

$$-7168x^{16-1}$$

Subtract 1 from 16.

$$-7168x^{15}$$