To divide the expression [tex]\(12 a^8 b^3\)[/tex] by [tex]\(3 a^2 b\)[/tex], follow these steps:
1. Divide the coefficients:
- The coefficient of the numerator is 12.
- The coefficient of the denominator is 3.
- Divide 12 by 3 to obtain [tex]\( \frac{12}{3} = 4\)[/tex].
2. Simplify the exponents of [tex]\(a\)[/tex]:
- The exponent of [tex]\(a\)[/tex] in the numerator is 8.
- The exponent of [tex]\(a\)[/tex] in the denominator is 2.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\( 8 - 2 = 6\)[/tex].
- Thus, [tex]\(a^8 / a^2 = a^6\)[/tex].
3. Simplify the exponents of [tex]\(b\)[/tex]:
- The exponent of [tex]\(b\)[/tex] in the numerator is 3.
- The exponent of [tex]\(b\)[/tex] in the denominator is 1.
- Subtract the exponent in the denominator from the exponent in the numerator: [tex]\( 3 - 1 = 2\)[/tex].
- Thus, [tex]\(b^3 / b = b^2\)[/tex].
Putting it all together, the simplified form of the expression is:
[tex]\[ 4 \cdot a^6 \cdot b^2 \][/tex]
Therefore, the correct answer is: [tex]\( 4 a^6 b^2 \)[/tex].
