The sides of a square are 2 to the power of 4÷9 inches long. what is the area of the square?

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The sides of a square are 2 to the power of 4÷9 inches long. what is the area of the square?

Algebra
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side = 2^(4/9) area = side^2 = ?
Wait what
How can I solve this??? @vocaloid

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Other answers:

it gives you the length of one side, so to find the area, you just square the length (side)*(side) = 2^(4/9) * 2^(4/9) = ?
Do I times it 4 times or just twice @vocaloid
twice..
I got 4 to the power of 16/81
not quite, we have to use the exponent rule here keep the base and add the exponents together 2^(4/9) * 2^(4/9) = 2^(4/9 + 4/9) = ?
Oh ok
Now I got 2 to the power of 8/9
Is that right? @vocaloid
yes, sorry for the late reply
Do you you think you can help me with another question? @vocaloid
sure
Given the function f(x) = 5^x , section A is from = x = 0 to x = 1 and the section B is from x = 2 to x = 3. Part A: Find The average rate of change of each section Part B: How many times greater is the average rate of change of section B then section A? Explain why one rate of change is greater than the other. @vocaloid
part A) we want two values 1. the rate of change between x = 0 and x = 1 and 2. the rate of change between x = 2 and x = 3 so, let's just tackle the first part for now the rate of change between x = 0 and x = 1 can be found using the formula [f(1)-f(0)]/(1-0)
I got one
not quite, let's take it bit by bit f(1) = ?
Is it one
not quite f(x) = 5^x f(1) = ?
5 to the power of one
right now f(0) = ?
5 to the power of zero
right, so [f(1)-f(0)]/(1-0) = ?
Is it 1/1
no... remember, we just calculated f(1) and f(0) f(1) - f(0) = ?
5^1 - 5^0
right, so [f(1)-f(0)]/(1-0) = ?
Do I have to solve the exponent
yes
5-1/ 1-0 = 4/1
right, and 4/1 = ?
4
right, now let's calculate the rate of change from x = 2 to x = 3 [f(3)-f(2)]/(3-2) = ?
5^3 - 5^2/ 3-2
right, keep going...
125 - 25/ 3-2
right, keep going...
100/1= 100
right
now we're finished w/ part A part B wants us to find (rate of change from x = 2 to x = 3)/(rate of change from x = 1 to x = 2) using what we calculated earlier... 100/4 = ?
25
right so section B is 25 times as great (24 times greater) as section A
So that's the answer
as for "explain why" I would say something along the lines of "f(x) is an increasing exponential function
yeah
Thank you

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