solve the equation. chech for extraneous solutions.

Question

how do i do this.
1.x1/4=2
2.x2/3=16
3.x1/2=8

Answer 1

Use the rules of exponents, for example:
x^a+b=x^a+x^b
x^a*b=(x^a)^b

x^1/4=2
raise to the fourth power on each side:
(x^1/4)^4=2^4
x^(1/4)*4=16
x=16

However, note that since 2^4=16, (-2)^4=16, the roots to the equation appear to be 2,-2.

Since we have squared both sides of the equation, twice, we need to check for extraneous roots (that may have been introduced because of squaring) by substituting the possible answers into the original equation.

We find that -2 is not a correct answer, thus an extraneous root.

The answer is therefore 2.

I will leave you to tackle the remaining questions.