Question

Simplify the expression if possible. $$\frac{14 x^{2}}{50 x^{4}}$$

Short answer

So, the simplified form of the given expression \(\frac{14x^{2}}{50x^{4}}\) is \(\frac{7}{25}x^{-2}\)

Step-by-step solution

Break Down the Expression

First, break down the given expression \(\frac{14 x^{2}}{50 x^{4}}\) into two fractions, one for the constants and one for the variables. So it becomes \(\frac{14}{50} \times \frac{x^{2}}{x^{4}}\)

Simplify the Constants

The numerical constants 14 and 50 have a common factor of 2, so you can simplify the fraction to \(\frac{7}{25}\). So, now we have \(\frac{7}{25} \times \frac{x^{2}}{x^{4}}\)

Simplify the Variables

Next, simplify the variables using the law of exponents which states that for any real number 'a' and any integers m and n, \(a^{m}\div a^{n} = a^{m-n}\). Therefore \(\frac{x^{2}}{x^{4}} = x^{2-4} = x^{-2}\)

Final Simplification

Combine the constants and variables again for the final simplified form. So, the simplified version of the given expression is \(\frac{7}{25} \times x^{-2}\)