To divide the rational expression, we need to simplify the rational fractions and then divide them.
First, let's simplify the expressions individually.
For the numerator: 2x^4 / 3y^3
The numerator is already simplified, so no further simplification is needed.
For the denominator: 8y^(-4/3) / x^(-6)
We can simplify the denominator by moving negative exponents to the numerator and changing their signs.
8y^(-4/3) / x^(-6) = 8 / (y^(4/3) * x^6)
Now that we have simplified the expressions, we can divide them by multiplying the first fraction by the reciprocal of the second fraction.
(2x^4 / 3y^3) / (8 / (y^(4/3) * x^6))
To divide, we multiply the first fraction by the reciprocal of the second fraction.
(2x^4 / 3y^3) * ((y^(4/3) * x^6) / 8)
When multiplying rational expressions, we can simplify by canceling common factors between the numerators and denominators.
Canceling factors:
(2x^4 / (3y^3)) * ((y^(4/3) * x^6) / 8)
= (2x^4 * y^(4/3) * x^6) / (3y^3 * 8)
To simplify further, we can combine like terms in the numerator and denominator.
= (2 * x^4 * x^6 * y^(4/3)) / (3 * 8 * y^3)
= (2 * x^(4 + 6) * y^(4/3)) / (24 * y^3)
= (2 * x^10 * y^(4/3)) / (24 * y^3)
Simplifying the expression gives us:
(x^10 * y^(4/3)) / (12 * y^3)
The restrictions on the variables are:
1. The variable y cannot equal zero since it appears in the denominator.
2. The variable x does not have any restrictions.
Divide and then simplify the rational expression. State any restrictions on the variable.
2x^4/3y^3 divided by 8y^-4/3x^-6
3 answers
where did those fractional powers come from?
2x^4/3y^3 divided by 8y^-4/3x^-6
= 2x^4/3y^3 * 3x^-6/8y^-4
= 2x^4/3y^3 * 3y^4/8x^6
= 6x^4y^4/24x^6y^3
= y/4x^2
x and y cannot be zero
2x^4/3y^3 divided by 8y^-4/3x^-6
= 2x^4/3y^3 * 3x^-6/8y^-4
= 2x^4/3y^3 * 3y^4/8x^6
= 6x^4y^4/24x^6y^3
= y/4x^2
x and y cannot be zero
You are correct, I apologize for the error in my previous response. The correct simplification of the rational expression is:
2x^4/3y^3 divided by 8y^(-4/3)x^(-6)
= 2x^4/3y^3 * 3y^(4/3)x^6/8
= 6x^10y^4/24x^6y^3
= x^4y/4y^2x^2
= y/4x^2
The restrictions on the variables are:
1. The variable y cannot equal zero since it appears in the denominator.
2. The variable x cannot be zero since it appears in the denominator.
2x^4/3y^3 divided by 8y^(-4/3)x^(-6)
= 2x^4/3y^3 * 3y^(4/3)x^6/8
= 6x^10y^4/24x^6y^3
= x^4y/4y^2x^2
= y/4x^2
The restrictions on the variables are:
1. The variable y cannot equal zero since it appears in the denominator.
2. The variable x cannot be zero since it appears in the denominator.