Question

simplify.
\frac{b^{5}a^{2}}{b^{3}a^{6}}

Explanation:

Step1: Simplify the \( b \)-terms

Using the quotient rule for exponents \( \frac{x^m}{x^n}=x^{m - n} \), for the \( b \)-terms: \( \frac{b^5}{b^3}=b^{5 - 3}=b^2 \)

Step2: Simplify the \( a \)-terms

For the \( a \)-terms: \( \frac{a^2}{a^6}=a^{2 - 6}=a^{-4} \) or \( \frac{1}{a^4} \)

Step3: Combine the results

Multiply the simplified \( b \)-term and \( a \)-term: \( b^2\times a^{-4}=\frac{b^2}{a^4} \)

Answer:

\( \frac{b^{2}}{a^{4}} \)