Victoria is finding the value of n for the equation 3/sqrt14^1/6 = 14^1/n

Question

Victoria writes 3/sqrt 14^1/6 = (14^1/6)^3 = 14^3/6= 14 1/2 so n=2
Is Victoria correct? Justify your answer.

Answer 1

Victoria is not correct. To justify this, let's break down her solution step by step:

1) Victoria starts by simplifying the expression on the left side of the equation: 3/sqrt(14^1/6).

2) She correctly simplifies the square root of (14^1/6) to (14^1/6)^1/2 = 14^1/12.

3) However, she then cubes (14^1/12) to get (14^3/12).

4) Lastly, Victoria mistakenly simplifies (14^3/12) to 14^3/6.

At this point, Victoria made an error in simplifying the exponent. The correct simplification would be:

(14^3/12) = (14^1/4) = sqrt(14^1/2).

So, the correct value of n is 4, not 2.