To find the quotient of the expression 6x4 ÷ 15x3 ÷ 2x2 ÷ 10x ÷ 4 ÷ 3x2 ÷ 2, we need to follow a systematic approach.
First, let’s simplify each term in the numerator and the denominator:
- Numerator: The numerator is simply 6x4.
- Denominator: The terms we have in the denominator are: 15x3, 2x2, 10x, 4, 3x2, and 2.
Now, we can combine all the denominator terms:
- 15 × 2 × 10 × 4 × 3 × 2
- Additionally, we will sum up the coefficients of the x terms:
- x3 + x2 + x + x + x2 = x3+2+1+1+2 = x9
Calculating the coefficient:
- 15 × 2 × 10 × 4 × 3 × 2 = 2400
This means our expression now looks like:
Numerator: 6x4
Denominator: 2400x9
Putting it all together, we have:
6x4 ÷ 2400x9 = 6/2400 x4 ÷ x9 = 6/2400 x4-9 = 6/2400 x-5
Finally:
- We can simplify the coefficient fraction: 6/2400 = 1/400.
Thus, the final quotient is:
1/400 x-5
Alternatively, this can also be expressed as:
1/400 × 1/x5 = 1/(400x5)
So, the final answer is:
1/(400x5)