Answer:
(c) Point A is not on a bisector
Step-by-step explanation:
The figure shows you AR > AT. Since AX is the same for both triangles, angle AXR must be greater than angle AXT. This means AX is not the bisector of angle X.
Since AT is perpendicular to XT, it cannot be the perpendicular bisector of XT. That bisector will intersect XT at its midpoint, not its end.
The marked distances show you that A is different distances from T and R.
The only statement that makes any sense is ...
Point A is not on a bisector.
Take to total number of people attending and subtract the number of adults. The remainder are the children
2,451 - 745 = 1,706
<h2>
Hello!</h2>
The answer is:
The second option,
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
<h2>
Why?</h2>
Discarding each given option in order to find the correct one, we have:
<h2>
First option,</h2>
![\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%7D%5Csqrt%5Bm%5D%7By%7D%3D%5Csqrt%5B2m%5D%7Bxy%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%7D%5Csqrt%5Bm%5D%7By%7D%3D%5Csqrt%5Bm%5D%7Bxy%7D)
<h2>
Second option,</h2>
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
The statement is true, we can prove it by using the following properties of exponents:

![\sqrt[n]{x^{m} }=x^{\frac{m}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%20%7D%3Dx%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%20%7D)
We are given the expression:
![(\sqrt[m]{x^{a} } )^{b}](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D)
So, applying the properties, we have:
![(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%28x%5E%7B%5Cfrac%7Ba%7D%7Bm%7D%7D%29%5E%7Bb%7D%3Dx%5E%7B%5Cfrac%7Bab%7D%7Bm%7D%7D%5C%5C%5C%5Cx%5E%7B%5Cfrac%7Bab%7D%7Bm%7D%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
Hence,
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
<h2>
Third option,</h2>
![a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}](https://tex.z-dn.net/?f=a%5Csqrt%5Bn%5D%7Bx%7D%2Bb%5Csqrt%5Bn%5D%7Bx%7D%3Dab%5Csqrt%5Bn%5D%7Bx%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}](https://tex.z-dn.net/?f=a%5Csqrt%5Bn%5D%7Bx%7D%2Bb%5Csqrt%5Bn%5D%7Bx%7D%3D%28a%2Bb%29%5Csqrt%5Bn%5D%7Bx%7D)
<h2>
Fourth option,</h2>
![\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5Bm%5D%7Bx%7D%20%7D%7B%5Csqrt%5Bm%5D%7By%7D%7D%3Dm%5Csqrt%7Bxy%7D)
The statement is false, the correct form of the statement (according to the property of roots) is:
![\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5Bm%5D%7Bx%7D%20%7D%7B%5Csqrt%5Bm%5D%7By%7D%7D%3D%5Csqrt%5Bm%5D%7B%5Cfrac%7Bx%7D%7By%7D%20%7D)
Hence, the answer is, the statement that is true is the second statement:
![(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }](https://tex.z-dn.net/?f=%28%5Csqrt%5Bm%5D%7Bx%5E%7Ba%7D%20%7D%20%29%5E%7Bb%7D%3D%5Csqrt%5Bm%5D%7Bx%5E%7Bab%7D%20%7D)
Have a nice day!