Solve 8x^10/6x^2

$$\frac { 8 x ^ { 10 } } { 6 x ^ { 2 } }$$

Evaluate

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

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8x^{10}\right)^{1}\times \frac{1}{6x^{2}}$$

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

$$8^{1}\left(x^{10}\right)^{1}\times \frac{1}{6}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{6}\left(x^{10}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$8^{1}\times \frac{1}{6}x^{10}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$8^{1}\times \frac{1}{6}x^{10}x^{-2}$$

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

$$8^{1}\times \frac{1}{6}x^{10-2}$$

Add the exponents 10 and -2.

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

Raise 8 to the power 1.

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

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

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

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{10}}{6^{1}x^{2}}$$

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

$$\frac{8^{1}x^{10-2}}{6^{1}}$$

Subtract 2 from 10.

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

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. x

$$\frac{32x^{7}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{6}x^{10-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}x^{8})$$

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}.

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

Do the arithmetic.

$$\frac{32}{3}x^{7}$$