To simplify the expression [tex]\(\frac{b^3 a^6}{b^5 a^4}\)[/tex], let's follow these steps:
1. Separate the bases and exponents:
The given expression can be separated into two parts: one involving [tex]\(b\)[/tex] and the other involving [tex]\(a\)[/tex]:
[tex]\[
\frac{b^3}{b^5} \times \frac{a^6}{a^4}
\][/tex]
2. Simplify each part by applying the division rule for exponents:
The division rule for exponents states that when dividing like bases, you subtract the exponents: [tex]\(\frac{x^m}{x^n} = x^{m-n}\)[/tex].
- For the base [tex]\(b\)[/tex]:
[tex]\[
\frac{b^3}{b^5} = b^{3-5} = b^{-2}
\][/tex]
- For the base [tex]\(a\)[/tex]:
[tex]\[
\frac{a^6}{a^4} = a^{6-4} = a^2
\][/tex]
3. Combine the simplified parts:
By combining the results from the previous step, we get:
[tex]\[
b^{-2} \times a^2
\][/tex]
So, the simplified expression is:
[tex]\[
b^{-2} a^2
\][/tex]
This means that the final simplified form of [tex]\(\frac{b^3 a^6}{b^5 a^4}\)[/tex] is [tex]\(b^{-2} a^2\)[/tex].
