Question

simplify, \\(dfrac{20x^4}{5x^5}\\)

Explanation:

Step1: Simplify the coefficients

We have the fraction \(\frac{20x^{4}}{5x^{5}}\). First, simplify the coefficients \(20\) and \(5\). Dividing \(20\) by \(5\) gives \(\frac{20}{5}=4\).

Step2: Simplify the variable terms

For the variable terms with the same base \(x\), we use the rule of exponents \( \frac{x^{m}}{x^{n}}=x^{m - n}\). Here, \(m = 4\) and \(n = 5\), so \(\frac{x^{4}}{x^{5}}=x^{4-5}=x^{-1}=\frac{1}{x}\) (since \(x^{-a}=\frac{1}{x^{a}}\) for \(x
eq0\)).

Step3: Combine the results

Now, combine the simplified coefficient and the simplified variable term. We had \(4\) from the coefficients and \(\frac{1}{x}\) from the variable terms, so multiplying them together gives \(4\times\frac{1}{x}=\frac{4}{x}\).

Answer:

\(\frac{4}{x}\)