Solve 6x^8/3x^3

$$\frac { 6 x ^ { 8 } } { 3 x ^ { 3 } }$$

Evaluate

$$2x^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6x^{8}\right)^{1}\times \frac{1}{3x^{3}}$$

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

$$6^{1}\left(x^{8}\right)^{1}\times \frac{1}{3}\times \frac{1}{x^{3}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{3}\left(x^{8}\right)^{1}\times \frac{1}{x^{3}}$$

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

$$6^{1}\times \frac{1}{3}x^{8}x^{3\left(-1\right)}$$

Multiply 3 times -1.

$$6^{1}\times \frac{1}{3}x^{8}x^{-3}$$

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

$$6^{1}\times \frac{1}{3}x^{8-3}$$

Add the exponents 8 and -3.

$$6^{1}\times \frac{1}{3}x^{5}$$

Raise 6 to the power 1.

$$6\times \frac{1}{3}x^{5}$$

Multiply 6 times \frac{1}{3}.

$$2x^{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{8}}{3^{1}x^{3}}$$

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

$$\frac{6^{1}x^{8-3}}{3^{1}}$$

Subtract 3 from 8.

$$\frac{6^{1}x^{5}}{3^{1}}$$

Divide 6 by 3.

$$2x^{5}$$

Differentiate w.r.t. x

$$10x^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{3}x^{8-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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}.

$$5\times 2x^{5-1}$$

Do the arithmetic.

$$10x^{4}$$