Simplify Each Expression. Rationalize all denominators. Assume that all variables are positive.
3 times the square root of 11x^3y (the three is an exponet) over -2 times the square root of 12x^4y (the 4 is an exponet)
square top and bottom.
3*sqrt(11x^3y)/-2*sqrt(12x^4y)=
9(11x^3y)/4(12x^4y) =
y cancels
x^3 cancels leaving x on the bottom.
9(11)/4(12x) =
Divide 9 and 12 by 3
3(11)/(4*4x) =
33/16x
Check my work carefully.
Actually, I figured it out.....
Because of what it says in the directions: Simplify Each Expression. Rationalize all denominators. Assume that all variables are positive, I have to rationalize all denominators, which means you can't have a radical in the denominator so you have to multiply the numerator and the denominator both by the denominator so......
3*sqrt of 11x^3 y (it is actually 11x cubed then the y follows but i did it this way to keep from confusing anybody) over -2*sqrt of 12x^4 y equals both the top and bottom times -2*sqrt of 12x^4 y which gives you negative 6*sqrt132x^7 y^2 over 4*sqrt24x^8 y^2 which simplified is 12x^4 y, then you multiply 4 by 12x^4 y which gives you -6*sqrt132x^7 y^2 over 48x^4, you then factor down as much as possible of what is under the square root, in this case, 132 can be broken down, using the factor tree to 2*sqrt of 33, this is because we are squaring so there has to be 2 of a number before you can bring it out like there were two 2s so i brought them out and this makes it were 2 is going to be multiplied by -6 12on the outside of the sqrt which gives you -12*sqrt of 33x^7 y^12 over 48x^4, then you break down the "x" and the "y", 2 goes into 7 three times so u bring a x^3 on the outside, the 2 goes into 12 six times so you bring y^6 on the outside which gives you -12x^3 y^6*sqrt of 33x over 48x^4 y, then the y^6 on top can be divided by the y on the bottom which gives you y^5 on top for the final answer of -12x^3 y^5*sqrt of 33x over 48x^4!
Thanks for the help anyway though!
To simplify the given expression, we need to rationalize the denominators of the fractions.
Let's start by rewriting the expression:
(3√(11x^3y)^3) / (-2√(12x^4y)^4)
Now, let's simplify the expression inside the square root:
(3√(11^3 * (x^3)^3 * y^3)) / (-2√(12^4 * (x^4)^4 * y^4))
Simplifying further, we get:
(3√(1331x^9y^3)) / (-2√20736x^16y^4)
To rationalize the denominator, we need to get rid of the square root in the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of -2√20736x^16y^4 is -2√20736x^16y^4. Multiplying by the conjugate, we get:
(3√(1331x^9y^3) * (-2√20736x^16y^4)) / (-2√20736x^16y^4 * -2√20736x^16y^4)
Now, let's simplify the expression:
((-6)√(1331x^9y^3 * 20736x^16y^4)) / (4 * 20736x^16y^4)
Simplifying further, we get:
((-6)√(2759237632x^25y^7)) / (82944x^16y^4)
Since all variables are assumed to be positive, we can simplify the expression by taking out the square root and dividing the exponents:
((-6)(x^12)(y^2)√(100768356x^9y^5)) / (82944x^16)
Simplifying further, we get the final answer:
(-6y^2√(100768356x^9y^5)) / (82944x^4)
So, the simplified expression with rationalized denominators is (-6y^2√(100768356x^9y^5)) / (82944x^4).