How do you simplify $(1/4)^(1/2)$ ?

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Answer 1 · 2017-01-29T10:35:49

$+-1/2$

$color(blue)("Demonstration of what this means using numbers")$

$5^(2/3) = root(3)(5^2)$

$5^(9/29)=root(29)(5^9)$
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$color(blue)("Answering the question")$

Given: $(1/4)^(1/2)$

This is the same as: $" "root(2)((1/4)^1)" " ->" "sqrt((1/4)^1)$

Note that anything raised to the power of 1 is itself so $(1/4)^1=1/4$
so now we have: $sqrt(1/4)$

This is the same as: $" "(sqrt(1))/(sqrt(4))=+-1/2$

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$color(blue)("Footnote")$

The answer has to be positive or negative.

$(-1/2)xx(-1/2)=+1/4$

$(+1/2)xx(+1/2)=+1/4$

How do you simplify (1/4)^(1/2)(1/4)^(1/2)?