Sure, let's simplify the given expression step by step.
The given expression is:
[tex]\[
\frac{a^4 b^3}{a^5 b^2}
\][/tex]
To simplify this, we need to handle the [tex]\(a\)[/tex] terms and the [tex]\(b\)[/tex] terms separately.
### Step 1: Simplify the [tex]\(a\)[/tex] terms
Look at the [tex]\(a\)[/tex] terms in the numerator and denominator:
[tex]\[
\frac{a^4}{a^5}
\][/tex]
Using the properties of exponents, specifically [tex]\( \frac{x^m}{x^n} = x^{m-n} \)[/tex], we get:
[tex]\[
\frac{a^4}{a^5} = a^{4-5} = a^{-1}
\][/tex]
Since [tex]\(a^{-1} = \frac{1}{a}\)[/tex], this simplifies to:
[tex]\[
\frac{1}{a}
\][/tex]
### Step 2: Simplify the [tex]\(b\)[/tex] terms
Next, look at the [tex]\(b\)[/tex] terms in the numerator and denominator:
[tex]\[
\frac{b^3}{b^2}
\][/tex]
Using the same property of exponents:
[tex]\[
\frac{b^3}{b^2} = b^{3-2} = b
\][/tex]
### Step 3: Combine the results
Now, combine the simplified [tex]\(a\)[/tex] and [tex]\(b\)[/tex] terms:
[tex]\[
\frac{a^4 b^3}{a^5 b^2} = \frac{1}{a} \times b = \frac{b}{a}
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
\frac{b}{a}
\][/tex]
