Solve -8x^4:(-4x^3)=

$$- 8 x ^ { 4 } : ( - 4 x ^ { 3 } ) =$$

Evaluate

$$2x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-8x^{4}\right)^{1}\times \frac{1}{-4x^{3}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-8\right)^{1}\left(x^{4}\right)^{1}\times \frac{1}{-4}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-8\right)^{1}\times \frac{1}{-4}\left(x^{4}\right)^{1}\times \frac{1}{x^{3}}$$

To raise a power to another power, multiply the exponents.

$$\left(-8\right)^{1}\times \frac{1}{-4}x^{4}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-8\right)^{1}\times \frac{1}{-4}x^{4}x^{-3}$$

To multiply powers of the same base, add their exponents.

$$\left(-8\right)^{1}\times \frac{1}{-4}x^{4-3}$$

Add the exponents 4 and -3.

$$\left(-8\right)^{1}\times \frac{1}{-4}x^{1}$$

Raise -8 to the power 1.

$$-8\times \frac{1}{-4}x^{1}$$

Raise -4 to the power -1.

$$-8\left(-\frac{1}{4}\right)x^{1}$$

Multiply -8 times -\frac{1}{4}.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-8\right)^{1}x^{4}}{\left(-4\right)^{1}x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(-8\right)^{1}x^{4-3}}{\left(-4\right)^{1}}$$

Subtract 3 from 4.

$$\frac{\left(-8\right)^{1}x^{1}}{\left(-4\right)^{1}}$$

Divide -8 by -4.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$

Differentiate w.r.t. x

$$2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{8}{-4}\right)x^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2x^{1-1}$$

Do the arithmetic.

$$2x^{0}$$

For any term t except 0, t^{0}=1.

$$2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2$$