Solve 6^2x^10/6^3x^2

$$\frac { 6 ^ { 2 } x ^ { 10 } } { 6 ^ { 3 } x ^ { 2 } }$$

Evaluate

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

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{6^{2}x^{10}}{6^{3}x^{2}}$$

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

$$6^{2-3}x^{10-2}$$

Subtract 3 from 2.

$$\frac{1}{6}x^{10-2}$$

Subtract 2 from 10.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Cancel out 6^{2}x^{2} in both numerator and denominator.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply 8 times \frac{1}{6}.

$$\frac{4}{3}x^{8-1}$$

Subtract 1 from 8.

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