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## Sagot :

### Step 1: Simplify the Coefficients

The fraction has coefficients 20 in the numerator and 4 in the denominator. Dividing these gives:

[tex]\[ \frac{20}{4} = 5 \][/tex]

### Step 2: Simplify the Powers of [tex]\(a\)[/tex]

The numerator has [tex]\(a^8\)[/tex] and the denominator has [tex]\(a^2\)[/tex]. When we divide powers of the same base, we subtract the exponents:

[tex]\[ a^8 \div a^2 = a^{8-2} = a^6 \][/tex]

### Step 3: Simplify the Powers of [tex]\(b\)[/tex]

The numerator has [tex]\(b^2\)[/tex] and the denominator has [tex]\(b\)[/tex] (which is [tex]\(b^1\)[/tex]). Again, we subtract the exponents:

[tex]\[ b^2 \div b^1 = b^{2-1} = b^1 = b \][/tex]

### Step 4: Combine the Results

Putting it all together, the simplified form of the expression [tex]\(\frac{20 a^8 b^2}{4 a^2 b}\)[/tex] is:

[tex]\[ 5 a^6 b \][/tex]

Thus, the equivalent expression is:

[tex]\[ 5 a^6 b \][/tex]

The correct answer is:

[tex]\[ \boxed{5 a^6 b} \][/tex]