What is the solution to the equation? Please explain the steps to this problem

16=(x-2)^(2/3

1 Answer
Jun 26, 2018

x=66

Explanation:

First, let's get rid of that nasty exponent. An exponent rule we can use is this:
a^(b/c)=root(c)(a^b)

Let's use it to simplify the right side of our equation:

(x-2)^(2/3) = root(3)((x-2)^2)

16=root(3)((x-2)^2)

Next, we need to remove the radical. Let's cube, or apply a power of 3, to each side. Here's how it will work:

(root(3)(a))^3 = a^(1/3*3)=a^(3/3)=a^1=a

We will apply this to our equation:

(16)^3=(root(3)((x-2)^2))^3
(16)^3=(x-2)^2
4096=(x-2)^2

Then, we will square each side. It works in the opposite way of the last step:

sqrt(a^2)=a^(2*1/2)=a^(2/2)=a^1=a

sqrt(4096)=sqrt((x-2)^2)

64=x-2

From here, we just add 2 to each side to get our answer:

64+2=x-2+2
66=x

Hope this helped you! Have a nice day!!!