Solve 8x^2/x^0

$$\frac { 8 x ^ { 2 } } { x ^ { 0 } }$$

Evaluate

$$8x^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8x^{2}\right)^{1}\times \frac{1}{x^{0}}$$

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

$$8^{1}\left(x^{2}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{0}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{1}\left(x^{2}\right)^{1}\times \frac{1}{x^{0}}$$

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

$$8^{1}\times \frac{1}{1}x^{2}x^{0}$$

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

$$8^{1}\times \frac{1}{1}x^{2}$$

Raise 8 to the power 1.

$$8\times \frac{1}{1}x^{2}$$

Differentiate w.r.t. x

$$16x$$

Steps Using Definition of a Derivative

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

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

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

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

$$16x$$