Posted by **Anonymous** on Saturday, May 8, 2010 at 9:09pm.

solve the equation. chech for extraneous solutions.

how do i do this.

1.x1/4=2

2.x2/3=16

3.x1/2=8

- math -
**MathMate**, Sunday, May 9, 2010 at 9:16am
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.

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