How do you express $t^(-2/7)$ in radical form?

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Answer 1 · 2018-06-03T22:24:19

See a solution process below:

We can rewrite this expression as:

$t^(-2 xx 1/7)$

Now, we can use this rule for exponents to rewrite the expression again:

$x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)$

$t^(color(red)(-2) xx color(blue)(1/7)) => (t^color(red)(-2))^color(blue)(1/7)$

Now, we can use this rule to write the expression in radical form:

$x^(1/color(red)(n)) = root(color(red)(n))(x)$

$(t^-2)^(1/color(red)(7)) => root(color(red)(7))(t^-2)$

If it is necessary to have no negative exponents we can use this rule of exponents to eliminate the negative exponent:

$x^color(red)(a) = 1/x^color(red)(-a)$

$root(7)(t^color(red)(-2)) => root(7)(1/t^color(red)(- -2)) => root(7)(1/t^color(red)(2))$

Or, because the $n$ th root of $1$ is always $1$

$1/root(7)(t^2)$

How do you express t^(-2/7)t^(-2/7) in radical form?