Solve (-18x^4):(6x^3)=

$$( - 18 x ^ { 4 } ) : ( 6 x ^ { 3 } ) =$$

Evaluate

$$-3x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-18x^{4}\right)^{1}\times \frac{1}{6x^{3}}$$

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

$$\left(-18\right)^{1}\left(x^{4}\right)^{1}\times \frac{1}{6}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$\left(-18\right)^{1}\times \frac{1}{6}\left(x^{4}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$\left(-18\right)^{1}\times \frac{1}{6}x^{4}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$\left(-18\right)^{1}\times \frac{1}{6}x^{4}x^{-3}$$

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

$$\left(-18\right)^{1}\times \frac{1}{6}x^{4-3}$$

Add the exponents 4 and -3.

$$\left(-18\right)^{1}\times \frac{1}{6}x^{1}$$

Raise -18 to the power 1.

$$-18\times \frac{1}{6}x^{1}$$

Multiply -18 times \frac{1}{6}.

$$-3x^{1}$$

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

$$-3x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-18\right)^{1}x^{4}}{6^{1}x^{3}}$$

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

$$\frac{\left(-18\right)^{1}x^{4-3}}{6^{1}}$$

Subtract 3 from 4.

$$\frac{\left(-18\right)^{1}x^{1}}{6^{1}}$$

Divide -18 by 6.

$$-3x^{1}$$

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

$$-3x$$

Differentiate w.r.t. x

$$-3$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{18}{6}\right)x^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{1})$$

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}.

$$-3x^{1-1}$$

Do the arithmetic.

$$-3x^{0}$$

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

$$-3$$