Question

select the equivalent expression.\\(\frac{x^{6}y^{5}}{x^{6}y^{4}}\\)\
answer\\(\frac{1}{y}\\) \\(y\\)\\(\frac{y}{x^{12}}\\) \\(\frac{x^{12}}{y}\\)

Explanation:

Step1: Simplify \(x\)-terms

For the \(x\)-terms, use the rule \(\frac{x^a}{x^b}=x^{a - b}\). Here, \(a = 6\), \(b = 6\), so \(\frac{x^6}{x^6}=x^{6 - 6}=x^0 = 1\) (since \(x^0 = 1\) for \(x
eq0\)).

Step2: Simplify \(y\)-terms

For the \(y\)-terms, use the same rule. \(a = 5\), \(b = 4\), so \(\frac{y^5}{y^4}=y^{5 - 4}=y^1 = y\).

Step3: Multiply the results

Multiply the simplified \(x\)-term and \(y\)-term: \(1\times y = y\).

Answer:

\(y\) (the option with \(y\))