Solve 800x^2/500x^2

$$\frac { 800 x ^ { 2 } } { 500 x ^ { 2 } }$$

Evaluate

$$\frac{8}{5}=1.6$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(800x^{2}\right)^{1}\times \frac{1}{500x^{2}}$$

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

$$800^{1}\left(x^{2}\right)^{1}\times \frac{1}{500}\times \frac{1}{x^{2}}$$

Use the Commutative Property of Multiplication.

$$800^{1}\times \frac{1}{500}\left(x^{2}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$800^{1}\times \frac{1}{500}x^{2}x^{2\left(-1\right)}$$

Multiply 2 times -1.

$$800^{1}\times \frac{1}{500}x^{2}x^{-2}$$

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

$$800^{1}\times \frac{1}{500}x^{2-2}$$

Add the exponents 2 and -2.

$$800^{1}\times \frac{1}{500}x^{0}$$

Raise 800 to the power 1.

$$800\times \frac{1}{500}x^{0}$$

Multiply 800 times \frac{1}{500}.

$$\frac{8}{5}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{8}{5}\times 1$$

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

$$\frac{8}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{800^{1}x^{2}}{500^{1}x^{2}}$$

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

$$\frac{800^{1}x^{2-2}}{500^{1}}$$

Subtract 2 from 2.

$$\frac{800^{1}x^{0}}{500^{1}}$$

For any number a except 0, a^{0}=1.

$$\frac{800^{1}}{500^{1}}$$

Reduce the fraction \frac{800}{500} to lowest terms by extracting and canceling out 100.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$