simplify
14a^8y^3-7a^4y^5+28a^12y^2/7a^4y
(4a^8Y^3 - 7a^4Y^5 + 28a^12Y^2) / 7a^4Y
14a^8Y^3 / 7a^4Y - 7a^4Y^5 / 7a^4Y +
28a^12Y^2 / 7a^4Y.
Divide each numerator by 7a^4Y:
2a^4Y^2 - Y^4 + 4a^8Y,
Factor out Y:
Y(2a^4Y - Y^3 + 4a^8).
To simplify the given expression, we can apply the basic rules of exponents and perform the necessary arithmetic operations.
First, let's rewrite the expression:
(14a^8y^3 - 7a^4y^5 + 28a^12y^2) / (7a^4y)
Let's simplify each term individually:
Term 1: 14a^8y^3 / (7a^4y)
When dividing terms with the same base, we subtract the exponents. In this case, a^8 / a^4 equals a^(8-4) which is a^4, and y^3 / y equals y^(3-1) which is y^2. So, term 1 simplifies to 2a^4y^2.
Term 2: -7a^4y^5 / (7a^4y)
Similarly, a^4 / a^4 equals a^(4-4) which is a^0, and y^5 / y equals y^(5-1) which is y^4. Since a^0 is equal to 1, term 2 simplifies to -y^4.
Term 3: 28a^12y^2 / (7a^4y)
Again, 28 / 7 equals 4, a^12 / a^4 equals a^(12-4) which is a^8, and y^2 / y equals y^(2-1) which is y. Thus, term 3 simplifies to 4a^8y.
Now that we have simplified each term, we can combine them:
2a^4y^2 - y^4 + 4a^8y