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.
Answer:
D. 20
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry</u>
- All angles in a triangle add up to 180°
Step-by-step explanation:
<u>Step 1: Set Up Equation</u>
3x + 3x + 10 + 2x + 10 = 180
<u>Step 2: Solve for </u><em><u>x</u></em>
- Combine like terms: 8x + 20 = 180
- Isolate <em>x</em> term: 8x = 160
- Isolate <em>x</em>: x = 20
Answer:
0.4
Step-by-step explanation:
If we count up all of the colored squares, we will get 28. And if we count the non-colored squares we will get 72.
Now, we take 28 and we divide it by 72. This will get us 0.3888888. That number rounded up is 0.4.
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Answer:
3x^2+5x+10
Step-by-step explanation:
add the x^2 and 2x^2