Certainly! Let's break down the solution to the given expression step-by-step:
[tex]\[ \frac{8 a^4 b^5}{2 a b} \][/tex]
1. Simplify the coefficients:
- The numerator has a coefficient of [tex]\( 8 \)[/tex].
- The denominator has a coefficient of [tex]\( 2 \)[/tex].
- Dividing the coefficients, we get:
[tex]\[ \frac{8}{2} = 4 \][/tex]
2. Simplify the powers of [tex]\( a \)[/tex]:
- The numerator has [tex]\( a^4 \)[/tex].
- The denominator has [tex]\( a \)[/tex].
- Using the rule [tex]\( \frac{a^m}{a^n} = a^{m-n} \)[/tex], we find:
[tex]\[ \frac{a^4}{a} = a^{4-1} = a^3 \][/tex]
3. Simplify the powers of [tex]\( b \)[/tex]:
- The numerator has [tex]\( b^5 \)[/tex].
- The denominator has [tex]\( b \)[/tex].
- Using the rule [tex]\( \frac{b^m}{b^n} = b^{m-n} \)[/tex], we find:
[tex]\[ \frac{b^5}{b} = b^{5-1} = b^4 \][/tex]
4. Combine the simplified parts:
- Now putting everything together, we get:
[tex]\[ 4 \cdot a^3 \cdot b^4 \][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ 4 a^3 b^4 \][/tex]
So, the final answer is:
[tex]\[ \boxed{4 a^3 b^4} \][/tex]
