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)