To simplify the given expression, let's break it down step-by-step:
Given expression:
[tex]\[
\frac{20 a^8 b^2}{4 a^2 b}
\][/tex]
1. Simplify the coefficients:
[tex]\[
\frac{20}{4} = 5
\][/tex]
2. Simplify the [tex]\( a \)[/tex] terms using the rule of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{a^8}{a^2} = a^{8-2} = a^6
\][/tex]
3. Simplify the [tex]\( b \)[/tex] terms using the rule of exponents [tex]\(\frac{b^m}{b^n} = b^{m-n}\)[/tex]:
[tex]\[
\frac{b^2}{b} = b^{2-1} = b
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
5 a^6 b
\][/tex]
Hence, the expression equivalent to the given expression
[tex]\[
\frac{20 a^8 b^2}{4 a^2 b}
\][/tex]
is:
[tex]\[
5 a^6 b
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{5 a^6 b}
\][/tex]
