Simplify:
3x^2 y^6 Z^2
------------ (dividided by)
4x^4 y^3 Z^4
my answer ?? 3y^2
--------
4x^2 Z^2
To simplify the given expression, you need to combine the like terms in the numerator and the denominator, and then simplify the resulting expression further if possible.
Let's break down the expression step by step:
1. Combine the like terms:
In the numerator, we have 3x^2, y^6, and Z^2.
In the denominator, we have 4x^4, y^3, and Z^4.
2. Simplify the like terms:
For the x terms, combine the exponents by subtracting the exponent of x in the denominator from the exponent of x in the numerator: x^2 - x^4 = x^(2 - 4) = x^-2 = 1/x^2.
For the y terms, combine the exponents by subtracting the exponent of y in the denominator from the exponent of y in the numerator: y^6 - y^3 = y^(6 - 3) = y^3.
Similarly, for the z terms, combine the exponents by subtracting the exponent of Z in the denominator from the exponent of Z in the numerator: Z^2 - Z^4 = Z^(2 - 4) = Z^-2 = 1/Z^2.
So, after combining the like terms, the simplified expression will become:
(3/x^2)(y^3)/(4Z^2).
3. Further simplify the expression:
If there is no common factor between the numerator and denominator, then the expression is already in its simplified form.
So, the final simplified form of the given expression is:
(3y^3) / (4x^2Z^2).
Therefore, your answer is:
3y^3
-------.
4x^2Z^2