To simplify
![\sqrt[4]{\dfrac{24x^6y}{128x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B24x%5E6y%7D%7B128x%5E4y%5E5%7D%7D)
we need to use the fact that
![\sqrt[4]{x^4}=|x|](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E4%7D%3D%7Cx%7C)
Why the absolute value? It's because 
.
We start by rewriting as
![\sqrt[4]{\dfrac{2^23x^6y}{2^6x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E6y%7D%7B2%5E6x%5E4y%5E5%7D%7D)
![\sqrt[4]{\dfrac{2^23x^4x^2y}{2^42^2x^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E4x%5E2y%7D%7B2%5E42%5E2x%5E4y%5E4y%7D%7D)
Since 
, we have 
, and the above reduces to
![\sqrt[4]{\dfrac{3x^2y}{2^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7B2%5E4y%5E4y%7D%7D)
Then we pull out any 4th powers under the radical, and simplify everything we can:
![\dfrac1{\sqrt[4]{2^4y^4}}\sqrt[4]{\dfrac{3x^2y}{y}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5B4%5D%7B2%5E4y%5E4%7D%7D%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7By%7D%7D)
![\dfrac1{|2y|}\sqrt[4]{3x^2}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%7C2y%7C%7D%5Csqrt%5B4%5D%7B3x%5E2%7D)
where 
allows us to write 
, and this also means that 
. So we end up with
![\dfrac{\sqrt[4]{3x^2}}{2y}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B4%5D%7B3x%5E2%7D%7D%7B2y%7D)
making the last option the correct answer.
Answer:
Pi/3 radians also measures 60 degrees not 30
Step-by-step explanation:
Pi/3 x 180/pi=180pi/3pi
Since both have pi they cancel out leaving 180/3, which equals 60.
10) 1 gallon of water for every inch of the fish's body length.
a) 2 1/2 inches long fish needs 2 1/2 gallon of water.
b) tank: l = 7 inches ; w = 5 inches; h = 7 ; volume = 7in * 5in * 7in = 245 in³
c) no. her fish tank is not large enough for the fish.
volume of 1 gallon of water is 231 in³, water needed is 2 1/2 gallon, so 5/2 * 231 in³ = 577.50 in³ volume.
11) volume = 7in * 3.5in * 1.75 in = 42.875 in³
weight of the brick = 0.1 pound per cubic inch ⇒ 42.875 in³ * 0.1 lb = 4.2875 pounds
weight of the gold bar = 0.7 pound per cubic inch ⇒ 42.875 in³ * 0.7 lb = 30.0125 pounds
12) l = 55cm ; w = 40cm ; h = 30 cm
volume = 55cm * 40cm * 30cm = 66,000 cm³
So we know there are 12 brown ones
brown=12
50 more than 12 is the number of clear bottles so 50+12=62
brown=12
clear=62
30 numbers down from 62 is the number of green ones so 62-30=32
brown=12
clear=62
green=32
12+62+32=106
so Yoshiko collected 106 bottles
