32 is the nearest whole number
Answer:
Option A.
Step-by-step explanation:
The given expression is,
![[(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}](https://tex.z-dn.net/?f=%5B%2864%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D)
By solving the given expression,
[Since
]


Now the expression will be,
![[(64)^{-\frac{1}{2}}]^{-\frac{2}{3}}=(\frac{1}{8})^{-\frac{2}{3}}](https://tex.z-dn.net/?f=%5B%2864%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5D%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D%28%5Cfrac%7B1%7D%7B8%7D%29%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D)

![={(\sqrt[3]{8})^2}](https://tex.z-dn.net/?f=%3D%7B%28%5Csqrt%5B3%5D%7B8%7D%29%5E2%7D)
= 2²
= 4
Therefore, value of the given expression will be 4.
Option (A) will be the answer.
Answer:
Please check the explanation.
Step-by-step explanation:
As we know that the average rate of change of f(x) in the closed
interval [a, b] is

Given the interval [a, b] = [0, 4]
as

∵ 


∵ 

so the average rate of change :



We know that a rate of change basically indicates how an output quantity changes relative to the change in the input quantity. Here, it is clear the value of y increase with the increase of input.
Is the 2 an exponent? if so, it is always an even integer.