Divide

6x^3y^6 / 24x^4y^3
_______ _________
16a^4b^2 14a^7b

I am not sure what the problem is exactly.

the second row is confusing me.

retype using brackets

To divide the given expression, you can follow these steps:

Step 1: Simplify the coefficients
The coefficients in the numerator and denominator are 6 and 24 respectively. To simplify them, divide both numbers by their greatest common factor, which is 6.

6 ÷ 6 = 1
24 ÷ 6 = 4

The simplified coefficients are 1 and 4.

Step 2: Simplify the variables
In the numerator, we have x raised to the power of 3 and y raised to the power of 6. In the denominator, we have x raised to the power of 4 and y raised to the power of 3. To simplify the variables, we subtract the exponents.

x^(3 - 4) = x^(-1) = 1/x
y^(6 - 3) = y^(3) = y^3

Step 3: Simplify the remaining coefficients and variables
Now, we are left with:

(1/4) * (1/x * y^3) / (16a^4b^2 * 14a^7b)

Step 4: Combine the variables
To combine the variables, we subtract the exponents of similar variables.

(1/4) * (y^3 / x) / (16a^(4 + 7) * b^(2 + 1))

Simplifying further:

(1/4) * (y^3 / x) / (16a^11 * b^3)

Step 5: Multiply the reciprocal
To divide by a fraction, we can multiply by its reciprocal. In this case, our second fraction is (16a^11 * b^3). Its reciprocal is (1 / (16a^11 * b^3)). So we can rewrite our expression as multiplication:

(1/4) * (y^3 / x) * (1 / (16a^11 * b^3))

Step 6: Simplify the expression
To simplify further, we multiply the coefficients and combine the variables.

(1 * y^3 * 1) / (4 * x * 16 * a^11 * b^3)

Simplifying the numerator and denominator:

y^3 / (64 * a^11 * b^3 * x)

So, the simplified expression is:

y^3 / (64a^11b^3x)