-1/3 It cant be the others because -1 is already at the edge and is not the number, 1/3 is positive but -1/3 is left of zero, therefore negative and 1 is right of zero, so is positive.
-1/3 is the correct answer.
Answer:
The equivalent expression for the given expression
is
![4x^{3} y^{2}(\sqrt[3]{4xy} )](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%20%29)
Step-by-step explanation:
Given:
![\sqrt[3]{256x^{10}y^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D)
Solution:
We will see first what is Cube rooting.
![\sqrt[3]{x^{3}} = x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%20x)
Law of Indices

Now, applying above property we get
![\sqrt[3]{256x^{10}y^{7} }=\sqrt[3]{(4^{3}\times 4\times (x^{3})^{3}\times x\times (y^{2})^{3}\times y )} \\\\\textrm{Cube Rooting we get}\\\sqrt[3]{256x^{10}y^{7} }= 4\times x^{3}\times y^{2}(\sqrt[3]{4xy}) \\\\\sqrt[3]{256x^{10}y^{7} }= 4x^{3}y^{2}(\sqrt[3]{4xy})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%5Csqrt%5B3%5D%7B%284%5E%7B3%7D%5Ctimes%204%5Ctimes%20%28x%5E%7B3%7D%29%5E%7B3%7D%5Ctimes%20x%5Ctimes%20%28y%5E%7B2%7D%29%5E%7B3%7D%5Ctimes%20y%20%20%20%29%7D%20%5C%5C%5C%5C%5Ctextrm%7BCube%20Rooting%20we%20get%7D%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204%5Ctimes%20x%5E%7B3%7D%5Ctimes%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29%20%5C%5C%5C%5C%5Csqrt%5B3%5D%7B256x%5E%7B10%7Dy%5E%7B7%7D%20%7D%3D%204x%5E%7B3%7Dy%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%29)
∴ The equivalent expression for the given expression
is
![4x^{3} y^{2}(\sqrt[3]{4xy} )](https://tex.z-dn.net/?f=4x%5E%7B3%7D%20y%5E%7B2%7D%28%5Csqrt%5B3%5D%7B4xy%7D%20%29)
Answer:
Step-by-step explanation:
Statements Reasons
1). ∠CXY ≅ ∠BXY 1). Given
2). ∠CAX ≅ ∠BAX 2). Given
3). AC ≅ AB 3). Given
4). AX ≅ AX 4). Reflexive property
5). ΔAXC ≅ ΔAXB 5). SAS property of congruence
6). CX ≅ BX 6). CPCTC
7). XY ≅ XY 7). Reflexive property
8). ΔYXB ≅ ΔYXC 8). SAS property of congruence
9). ∠XCY ≅ ∠XBY 9). CPCTC
Answer:
The ratio of sixth-grade students to fifth-grade students on the team was <u>7 : 8</u>.
Step-by-step explanation:
Given:
The girl's basketball team had 8 fifth-grade students and 7 sixth-grade students.
Now, to find the ratio of sixth-grade students to fifth-grade students on the team.
<em>Number of fifth-grade students = 8.</em>
<em>Number of sixth-grade students = 7.</em>
Now, to get the ratio of sixth-grade students to fifth-grade students on the team :


Therefore, the ratio of sixth-grade students to fifth-grade students on the team was 7 : 8.