Solve 10x^8/5x^2

$$\frac { 10 x ^ { 8 } } { 5 x ^ { 2 } }$$

Evaluate

$$2x^{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10x^{8}\right)^{1}\times \frac{1}{5x^{2}}$$

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

$$10^{1}\left(x^{8}\right)^{1}\times \frac{1}{5}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{5}\left(x^{8}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$10^{1}\times \frac{1}{5}x^{8}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$10^{1}\times \frac{1}{5}x^{8}x^{-2}$$

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

$$10^{1}\times \frac{1}{5}x^{8-2}$$

Add the exponents 8 and -2.

$$10^{1}\times \frac{1}{5}x^{6}$$

Raise 10 to the power 1.

$$10\times \frac{1}{5}x^{6}$$

Multiply 10 times \frac{1}{5}.

$$2x^{6}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}x^{8}}{5^{1}x^{2}}$$

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

$$\frac{10^{1}x^{8-2}}{5^{1}}$$

Subtract 2 from 8.

$$\frac{10^{1}x^{6}}{5^{1}}$$

Divide 10 by 5.

$$2x^{6}$$

Differentiate w.r.t. x

$$12x^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{5}x^{8-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$12x^{5}$$