Question

Solve the equation with rational exponents. (x minus 1 )Superscript 2 divided by 3 Baseline equals 64

Answer 1

`x=513 \Rightarrow S=\{513\}`

Explanation:

1) Rewriting for the sake of clarity:

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

2) To solve it, we need to turn the rational exponent equal to 1 via exponent rule of product. Multiplying 2/3 by its reciprocal 3/2 we get 1, since this is an equality we need to do it on the other side.

`(x-1)^{(2)/(3)}=64\\\\((x-1)^{(2)/(3)}]^{(3)/(2)}=(64)^{(3)/(2)}\\(x-1)=\sqrt{64^(3)}\\x-1+1=512+1\\x=513`