Solve 14x^6/63x^3

$$\frac { 14 x ^ { 6 } } { 63 x ^ { 3 } }$$

Evaluate

$$\frac{2x^{3}}{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(14x^{6}\right)^{1}\times \frac{1}{63x^{3}}$$

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

$$14^{1}\left(x^{6}\right)^{1}\times \frac{1}{63}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$14^{1}\times \frac{1}{63}\left(x^{6}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$14^{1}\times \frac{1}{63}x^{6}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$14^{1}\times \frac{1}{63}x^{6}x^{-3}$$

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

$$14^{1}\times \frac{1}{63}x^{6-3}$$

Add the exponents 6 and -3.

$$14^{1}\times \frac{1}{63}x^{3}$$

Raise 14 to the power 1.

$$14\times \frac{1}{63}x^{3}$$

Multiply 14 times \frac{1}{63}.

$$\frac{2}{9}x^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}x^{6}}{63^{1}x^{3}}$$

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

$$\frac{14^{1}x^{6-3}}{63^{1}}$$

Subtract 3 from 6.

$$\frac{14^{1}x^{3}}{63^{1}}$$

Reduce the fraction \frac{14}{63} to lowest terms by extracting and canceling out 7.

$$\frac{2}{9}x^{3}$$

Differentiate w.r.t. x

$$\frac{2x^{2}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14}{63}x^{6-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{9}x^{3})$$

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}.

$$3\times \frac{2}{9}x^{3-1}$$

Do the arithmetic.

$$\frac{2}{3}x^{2}$$