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)#