Answer:
Step-by-step explanation:
This problem could keep you going for quite a while. My suggestion is that you go get a cup of coffee and sip it slowly as you read this.
<em><u>Equation One</u></em>
Sqrt(x - 1)^3 = 8
(x - 1)^(3/2) = 8
Square both sides to get rid of the 2.
(x - 1)^3 = 8^2
(x - 1)^3 = 64
Now take the cube root of both sides to get rid of the 3 on the left
x - 1 = cuberoot(64)
x - 1 = 4 Add 1 to both sides
x - 1+1 = 4 + 1
x = 5
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<em><u>Second Equation</u></em>
4th root (x - 3)^5 = 32
Take the 5th root of both sides.
4th root(x - 3) = 2
This can be written as (x - 3)^(1/4) = 2
Now take the 4th power of both sides.
(x - 3) = 2^4
x - 3 = 16
add 3 to both sides.
x = 16 + 3
x = 19
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<em><u>Equation 3</u></em>
(x - 4)^(3/2) = 125
Take the cube root of both sides
(x - 4)^(1/2) = 125^(1/3) 1/3 is the cube root of something
(x - 4)^(1/2) = 5
square both sides to get rid of the 2
(x - 4) = 5^2
x - 4 = 25
Add 4 to both sides.
x = 25 + 4
x = 29
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<em><u>Fourth Equation</u></em>
(x + 2)^(4/3) = 16
take the 4th root of both sides
(x + 2) ^(1/3) = 16^(1/4)
(x + 2)^(1/3) = 2
Cube both sides
(x + 2) = 2^3
x + 2 = 8
Subtract 2 from both sides
x + 2 - 2 = 8-2
x = 6
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The first step is the most critical. You must look at what you are going to take the root of. When you do, for this question, it must come out even.
