Question

How do you solve `(x - 2) ^ { 2/ 3} = 64`?

Answer 1

Raise both sides of the equation to the power of 3/2.

Explanation:

We can cancel out exponents by raising them to their reciprocals, as the reciprocal of a number times the number always equals 1.

You may often do this without realizing it- it's the principle behind squaring a square root to remove the root entirely.

`(sqrt(x-74))^2=x-74`, because taking the square root of an expression is the same as taking the expression to the power of 1/2.

In the context of your equation, we can cancel out the exponent of 2/3 by raising both sides to the power of 3/2. The exponents on the left side multiply together due to rules of exponents, and we receive:

`(x-2)^(6/6)=(x-2)^1=64^(3/2)`

Now we just need to evaluate `64^(3/2)`. I'd recommend using your calculator.

`(x-2)=512`

`x=514`