Question

simplify.
\\(\frac{b^{4}a^{3}}{b^{6}a^{2}}\\)

Explanation:

Step1: Simplify the \(a\)-terms using the quotient rule for exponents (\( \frac{a^m}{a^n} = a^{m - n} \))

For the \(a\)-terms, we have \( \frac{a^3}{a^2} = a^{3 - 2} = a^1 = a \)

Step2: Simplify the \(b\)-terms using the quotient rule for exponents

For the \(b\)-terms, we have \( \frac{b^4}{b^6} = b^{4 - 6} = b^{-2} \)

Step3: Rewrite \(b^{-2}\) as a positive exponent

Recall that \( b^{-n} = \frac{1}{b^n} \), so \( b^{-2} = \frac{1}{b^2} \)

Step4: Combine the simplified \(a\)- and \(b\)-terms

Putting it together, we have \( \frac{a}{b^2} \)

Answer:

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