<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>
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,
<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:
Have a nice day!
Answer:
1.14226% decrease
Step-by-step explanation:
nearest to the would be a 1.1423 % decrease
Answer:The equation of a line is y = mx + b where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. (Remember that the slope is the steepness of a line and the y-intercept is the point where the line intersects the y-axis. The x- and y-coordinates are values of the points on the line of y = 3x - 1.)
Step-by-step explanation:
Lol yeah frrrrr im tryna get help with my Spanish
Answer:
a*(20-a)
Step-by-step explanation:
Let's assume that the length of the garden is a the width is b and the area is s.
b = 40/2 - a = 20-a
s =a*(20-a)=-a^2+20a=-(a-10)^2+100
then,
when a=10, max(-(a-10)^2) =0, max(s)=100
