Question

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

Answer 1

Answer:

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

Step-by-step explanation:

1) Rewriting for the sake of clarity:

$(x-1)^{\frac{2}{3}}=64$

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.

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