Megan:
x to the one third power =
![x ^{1/3}](https://tex.z-dn.net/?f=x%20%5E%7B1%2F3%7D%20)
<span>x to the one twelfth power = </span>
![x ^{1/12}](https://tex.z-dn.net/?f=x%20%5E%7B1%2F12%7D%20)
<span>The quantity of x to the one third power, over x to the one twelfth power is:
</span>
![\frac{x ^{1/3}}{x ^{1/12}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%5E%7B1%2F3%7D%7D%7Bx%20%5E%7B1%2F12%7D%7D%20)
<span>
Since </span>
![\frac{ x^{a} }{ x^{b} } = x ^{a-b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20x%5E%7Ba%7D%20%7D%7B%20x%5E%7Bb%7D%20%7D%20%3D%20x%20%5E%7Ba-b%7D%20)
then
![\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%5E%7B1%2F3%7D%7D%7Bx%20%5E%7B1%2F12%7D%7D%20%3D%20x%5E%7B1%2F3-1%2F12%7D%20)
Now, just subtract exponents:
1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4
![\frac{x ^{1/3}}{x ^{1/12}} = x^{1/3-1/12} = x^{1/4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%5E%7B1%2F3%7D%7D%7Bx%20%5E%7B1%2F12%7D%7D%20%3D%20x%5E%7B1%2F3-1%2F12%7D%20%3D%20x%5E%7B1%2F4%7D%20)
Julie:
x times x to the second times x to the fifth = x * x² * x⁵
<span>The thirty second root of the quantity of x times x to the second times x to the fifth is
</span>
![\sqrt[32]{x* x^{2} * x^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%20)
<span>
Since </span>
![x^{a}* x^{b}= x^{a+b}](https://tex.z-dn.net/?f=%20x%5E%7Ba%7D%2A%20x%5E%7Bb%7D%3D%20x%5E%7Ba%2Bb%7D%20)
Then
![\sqrt[32]{x* x^{2} * x^{5} }= \sqrt[32]{ x^{1+2+5} } =\sqrt[32]{ x^{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7Bx%2A%20x%5E%7B2%7D%20%2A%20x%5E%7B5%7D%20%7D%3D%20%5Csqrt%5B32%5D%7B%20x%5E%7B1%2B2%2B5%7D%20%7D%20%3D%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D)
Since
![\sqrt[n]{x^{m}} = x^{m/n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20%3D%20x%5E%7Bm%2Fn%7D%20%7D%20)
Then
![\sqrt[32]{ x^{8} }= x^{8/32} = x^{1/4}](https://tex.z-dn.net/?f=%5Csqrt%5B32%5D%7B%20x%5E%7B8%7D%20%7D%3D%20x%5E%7B8%2F32%7D%20%3D%20x%5E%7B1%2F4%7D%20)
Since both Megan and Julie got the same result, it can be concluded that their expressions are equivalent.
Well, seeing as how she mixed the clay, she has a total of 2 2/8 pounds clay (unsimplified). Although we don't know how many students she has in one class, with simple division of this number we can figure out how many student can finish the project. Removing the 2/8, we can already tell 2 students can do it, so that's a start. Now to divide the 2 pounds into 8ths. Each pound is enough for 8 students, so the 2 pounds totals to 16. Now add the extra 2 students, it's 18 total students. Hope I explained it well enough!
Answer:
![-3n](https://tex.z-dn.net/?f=-3n)
Step-by-step explanation:
"The product of negative three and a number." can be written as -3n, or -3 * n, where n is "the number".
Answer:
D.
Step-by-step explanation:
n is between -3 and 1, with 3 and 1 not included.
You need open dots on -3 and 1, and shading in between.
Answer: D.