Question

simplify. \\(\frac{b^{3}a^{6}}{b^{5}a^{4}}\\)

Explanation:

Step1: Simplify \(a\) terms

For the \(a\) variables, we use the quotient rule of exponents \(\frac{x^m}{x^n}=x^{m - n}\). Here, \(m = 6\) and \(n = 4\), so \(\frac{a^{6}}{a^{4}}=a^{6 - 4}=a^{2}\).

Step2: Simplify \(b\) terms

For the \(b\) variables, using the same quotient rule of exponents \(\frac{x^m}{x^n}=x^{m - n}\), with \(m = 3\) and \(n = 5\), we get \(\frac{b^{3}}{b^{5}}=b^{3 - 5}=b^{-2}\). But \(b^{-2}=\frac{1}{b^{2}}\), so combining with the \(a\) term, we have \(a^{2}\times\frac{1}{b^{2}}=\frac{a^{2}}{b^{2}}\).

Answer:

\(\frac{a^{2}}{b^{2}}\)