Solve 6x^9/2x^8

$$\frac { 6 x ^ { 9 } } { 2 x ^ { 8 } }$$

Evaluate

$$3x$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6x^{9}\right)^{1}\times \frac{1}{2x^{8}}$$

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

$$6^{1}\left(x^{9}\right)^{1}\times \frac{1}{2}\times \frac{1}{x^{8}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{2}\left(x^{9}\right)^{1}\times \frac{1}{x^{8}}$$

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

$$6^{1}\times \frac{1}{2}x^{9}x^{8\left(-1\right)}$$

Multiply 8 times -1.

$$6^{1}\times \frac{1}{2}x^{9}x^{-8}$$

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

$$6^{1}\times \frac{1}{2}x^{9-8}$$

Add the exponents 9 and -8.

$$6^{1}\times \frac{1}{2}x^{1}$$

Raise 6 to the power 1.

$$6\times \frac{1}{2}x^{1}$$

Multiply 6 times \frac{1}{2}.

$$3x^{1}$$

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

$$3x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{9}}{2^{1}x^{8}}$$

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

$$\frac{6^{1}x^{9-8}}{2^{1}}$$

Subtract 8 from 9.

$$\frac{6^{1}x^{1}}{2^{1}}$$

Divide 6 by 2.

$$3x^{1}$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{2}x^{9-8})$$

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.

$$3\times 1$$

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

$$3$$