The word partition means "division into shares". In Math, partition in number theory is a method of writing numbers as a sum of positive integers. Each integer is called a part or a summand. The order of the summand matters, thus making the sum a composition.
Partition function represents the possible number of partitions of a number (natural number <em>n</em>), or the number of distinct and order-independent methods of illustrating n as a sum of natural numbers.
Young diagram can be used to represent integer partitions.
Partition of numbers is taught to children specially the young ones to split large numbers to smaller units. This can be done in four different ways. For instance: 1 + 4, 1 + 1+ 1 + 2, 1 +3 +1 and 3 + 1 + 1.
Answer:
![4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )](https://tex.z-dn.net/?f=4%5Csqrt%5B3%5D%7B2%7Dx%28%5Csqrt%5B3%5D%7By%7D%2B3xy%5Csqrt%5B3%5D%7By%7D%20%29)
Step-by-step explanation:
Let's start by breaking down each of the radicals:
![\sqrt[3]{16x^3y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D)
Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of
, and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:
![\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot8%5Ccdot%20x%5E3%5Ccdot%20y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7B8%7D%20%5Csqrt%5B3%5D%7Bx%5E3%7D%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Ccdot2x%5Ccdot%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D2x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D)
We can apply this same technique of "extracting cubes" to the second term:
![\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot27%5Ccdot%20%28x%5E2%29%5E3%5Ccdot%20y%5E3%5Ccdot%20y%5E2%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7B%28x%5E2%29%5E3%7D%20%5Csqrt%5B3%5D%7By%5E3%7D%20%5Csqrt%5B3%5D%7By%5E2%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Ccdot%203%5Ccdot%20x%5E2%5Ccdot%20y%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E2%7D%20%5C%5C%3D3x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D)
Replacing those two expressions in the parentheses leaves us with this monster:
![2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})](https://tex.z-dn.net/?f=2%282x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D%29%2B4%283x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D%29)
What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:
![4, \sqrt[3]{2} , x](https://tex.z-dn.net/?f=4%2C%20%5Csqrt%5B3%5D%7B2%7D%20%2C%20x)
We can factor those out to give us a final, simplified expression:
![4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )](https://tex.z-dn.net/?f=4%5Csqrt%5B3%5D%7B2%7Dx%28%5Csqrt%5B3%5D%7By%7D%2B3xy%5Csqrt%5B3%5D%7By%7D%20%29)
Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.
Answer:
The coordinates of Jedd's house is (-5, 0)
Step-by-step explanation:
Given;
Location of Holli's House = (−1, 4)
Location of fast food restaurant = (−3, 2)
To Find:
The coordinate of Jedd's house.
Solution:
If the distance between the two points
and
is divided by the point (x,y) in the ratio of m : n then


Hollis house is located at (-1 , 4)
So, 
She walks in a straight line to get to Jedds house
The restaurant is located at (-3 , 2) and partitions the way from
(x , y) = (-3 , 2)
The ratio of Hollis house to Jedds house is 1 : 1
(m : n) = 1 : 2
Lets consider that Jedds house is located at 
Then
will be






Now
will be






∴ The coordinates of Jedd's house is (-5, 0)
in decimal formation it is -0.5 and in fraction -1/2
Is p5 really p^5?????????????