I don't understand :/ ?

Question

So the problem I have is (x-4)^2/3=100. I used the "help me solve this" feature and it gave me:

 

((x-4)^2/3)^3/2=+-(100)^3/2

 

and that gave me:

 

x-4=+-1000

 

 

I know how you got x-4 by multiplying by the reciprocal and it cancels them out but how do you get 1000 from (100)^3/2 ?

 

another question gave me:

 

((x-1)^2/3)^3/2 =+-(81)^3/2

 

and it equaled:

 

x-1=729 

 

I just don't understand what you have to do to solve the right side of the equation.

 

Answer 1

Jasmin - It is a tricky question, but very simple if we stick with the basics. Here is how we can approach:

 

Step - 1: - Let us eliminate the power 2/3 so raise both sides of the equation to the power 3/2. Once we do that we get:

 

x - 4 = (100) ^3/2

 

Step -2:

 

100 can be written as (10)² 

That would make 2 x 3/2 = 3 (multiplying the powers 2 and 3/2 - Power Rule!)

And (10)^{3 = 1000}

 

Step - 3: So, the question boils down to x - 4 = 1000 which implies that x = 1000 + 4 = 1004. That is the answer!

 

You can verify the answer : (1004 - 4)^2/3     

which is essentially 1000 or (10)^{3 with the 2/3 power.} 

And that eventually boils down to 100 which in your RHS (Right Hand Side) of the euqtaion

Answer 2

okay - lets break that out  = 100 ^3/2= = 100 ^1/2 X 3

^{= 10*10 *10 = 1000}

Answer 3

the exponent ^1/2 is the same as √, i.e 100^3/2 = 100³ = 1 000 000^1/2 = √1 000 000 = 1 000...

same for ^1/3 this simply means take the cube root, etc.

Answer 4

You aren't multiplying by the reciprocal.  You are raising the expressions to the reciprocal power.  Fractional exponents, like 1/2, are like taking the square root of the number.  So 100^3/2 power is same as the square root of 100³.  100 cubed is 1000000 and the square root of a million is 1000.

Answer 5

100^3/2 means "the square root of 100 cubed." So square root of 100 is +/-10, and +/-10 cubed is +/-1000.

 

So now you have x-4=-1000 and x-4=1000.

So x=-996 or 1004.

 

Second problem: 81^3/2: first take the square root of 81, which is -/+9. Then cube it, which is -/+729.

So you have x-1=-729 and x-1=729.

So x=728 and x=730.