The simplest radical form of the expression is
.
<h3>What is the simplification of power indices?</h3>
When we have indices in the form
, we are going to find the cube root of the (ax)². This can be mathematically expressed as:
![\mathbf{=(\sqrt[3]{ax})^2 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%28%5Csqrt%5B3%5D%7Bax%7D%29%5E2%20%7D)
From the given information:

![\mathbf{=(\sqrt[3]{8x^55y^3} } )^2](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%28%5Csqrt%5B3%5D%7B8x%5E55y%5E3%7D%20%7D%20%29%5E2)
![\mathbf{=(\sqrt[3]{40x^5y^3} } )^2](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%28%5Csqrt%5B3%5D%7B40x%5E5y%5E3%7D%20%7D%20%29%5E2)
![= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2](https://tex.z-dn.net/?f=%3D%20%28%5Csqrt%5B3%5D%7B40x%5E5%7D%20%5Ctimes%20%20%5Csqrt%5B3%5D%7By%7D%5E3%29%5E2)


Learn more about indices here:
brainly.com/question/170984
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Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.
Given the function is
and the Rolle's Theorem does not apply to the function.
Rolle's theorem is used to determine if a function is continuous and also differentiable.
The condition for Rolle's theorem to be true as:
- f(a)=f(b)
- f(x) must be continuous in [a,b].
- f(x) must be differentiable in (a,b).
To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.
If we look closely at the given function we can see that the first derivative of the given function is:
![\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%28x%29%26%3D%5Csqrt%7B%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E3%7D%5C%5C%20f%28x%29%26%3D%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C%20f%27%28x%29%26%3D%5Cfrac%7B3%7D%7B2%7D%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot%20%5Cfrac%7B2%7D%7B3%7D%5Ccdot%20%28-x%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%20f%27%28x%29%26%3D%5Cfrac%7B-%5Csqrt%7B2-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D%5Cend)
From this point of view we can see that the given function is not defined for x=0.
Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.
Learn more about Rolle's Theorem from here brainly.com/question/12279222
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#1: 4*5 + 4*6=20+24=44
#2: 4*(5+6)=4*11=44
Answer:
the answer is D
Step-by-step explanation:
i got it right