Solve 6x^7/3x^4

$$\frac { 6 x ^ { 7 } } { 3 x ^ { 4 } }$$

Evaluate

$$2x^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6x^{7}\right)^{1}\times \frac{1}{3x^{4}}$$

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

$$6^{1}\left(x^{7}\right)^{1}\times \frac{1}{3}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{3}\left(x^{7}\right)^{1}\times \frac{1}{x^{4}}$$

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

$$6^{1}\times \frac{1}{3}x^{7}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$6^{1}\times \frac{1}{3}x^{7}x^{-4}$$

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

$$6^{1}\times \frac{1}{3}x^{7-4}$$

Add the exponents 7 and -4.

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

Raise 6 to the power 1.

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

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

$$2x^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{7}}{3^{1}x^{4}}$$

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

$$\frac{6^{1}x^{7-4}}{3^{1}}$$

Subtract 4 from 7.

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

Divide 6 by 3.

$$2x^{3}$$

Differentiate w.r.t. x

$$6x^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{3}x^{7-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$6x^{2}$$