Question

simplify.
\\(\dfrac{a^{2}b^{4}}{2a^{3}b^{5}x^{5}}\\)

Explanation:

Step1: Simplify \(a\) terms

For the variable \(a\), we use the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\). Here, \(m = 2\) and \(n=2\), so \(\frac{a^{2}}{a^{2}}=a^{2 - 2}=a^{0} = 1\) (since \(a^{0}=1\) for \(a
eq0\)).

Step2: Simplify \(b\) terms

For the variable \(b\), using the same exponent rule \(\frac{a^m}{a^n}=a^{m - n}\), with \(m = 4\) and \(n = 3\), we get \(\frac{b^{4}}{b^{3}}=b^{4-3}=b^{1}=b\).

Step3: Simplify \(x\) terms

For the variable \(x\), since there is no \(x\) in the numerator, we can write the numerator as having \(x^{0}\) (because \(x^{0}=1\) for \(x
eq0\)). Then using the exponent rule \(\frac{x^{0}}{x^{5}}=x^{0 - 5}=x^{-5}=\frac{1}{x^{5}}\) (by the definition of negative exponents \(a^{-n}=\frac{1}{a^{n}}\)).

Step4: Combine the results

Multiply the results from the simplification of \(a\), \(b\), and \(x\) terms. We have \(1\times b\times\frac{1}{x^{5}}=\frac{b}{x^{5}}\).

Answer:

\(\frac{b}{x^{5}}\)