Solve (14x^4)div(2x^3)

$$( 14 x ^ { 4 } ) \div ( 2 x ^ { 3 } )$$

Evaluate

$$7x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(14x^{4}\right)^{1}\times \frac{1}{2x^{3}}$$

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

$$14^{1}\left(x^{4}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$14^{1}\times \frac{1}{2}\left(x^{4}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$14^{1}\times \frac{1}{2}x^{4}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$14^{1}\times \frac{1}{2}x^{4}x^{-3}$$

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

$$14^{1}\times \frac{1}{2}x^{4-3}$$

Add the exponents 4 and -3.

$$14^{1}\times \frac{1}{2}x^{1}$$

Raise 14 to the power 1.

$$14\times \frac{1}{2}x^{1}$$

Multiply 14 times \frac{1}{2}.

$$7x^{1}$$

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

$$7x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}x^{4}}{2^{1}x^{3}}$$

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

$$\frac{14^{1}x^{4-3}}{2^{1}}$$

Subtract 3 from 4.

$$\frac{14^{1}x^{1}}{2^{1}}$$

Divide 14 by 2.

$$7x^{1}$$

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

$$7x$$

Differentiate w.r.t. x

$$7$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14}{2}x^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1})$$

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}.

$$7x^{1-1}$$

Do the arithmetic.

$$7x^{0}$$

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

$$7\times 1$$

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

$$7$$