To find the quotient of the expression [tex]\(\frac{15 a^4 b^3}{12 a^2 b}\)[/tex], follow these steps:
1. Simplify the coefficients:
- The coefficient in the numerator is 15, and the coefficient in the denominator is 12.
- When you divide 15 by 12, you get [tex]\( \frac{15}{12} = 1.25 \)[/tex].
2. Simplify the expression's variable [tex]\(a\)[/tex]:
- In the numerator, [tex]\(a\)[/tex] has an exponent of 4, and in the denominator, [tex]\(a\)[/tex] has an exponent of 2.
- When you subtract the exponent of [tex]\(a\)[/tex] in the denominator from the exponent of [tex]\(a\)[/tex] in the numerator, you get [tex]\(4 - 2 = 2\)[/tex].
- So, [tex]\(a^4 / a^2 = a^2\)[/tex].
3. Simplify the expression's variable [tex]\(b\)[/tex]:
- In the numerator, [tex]\(b\)[/tex] has an exponent of 3, and in the denominator, [tex]\(b\)[/tex] has an exponent of 1.
- When you subtract the exponent of [tex]\(b\)[/tex] in the denominator from the exponent of [tex]\(b\)[/tex] in the numerator, you get [tex]\(3 - 1 = 2\)[/tex].
- So, [tex]\(b^3 / b = b^2\)[/tex].
Putting it all together, the simplified expression is [tex]\(1.25 a^2 b^2\)[/tex].
Therefore, the quotient of [tex]\(\frac{15 a^4 b^3}{12 a^2 b}\)[/tex] is [tex]\(\boxed{1.25 a^2 b^2}\)[/tex].
