Question

write the expression shown below in radical form.
$t^{\frac{1}{8}}$
$t^{\frac{1}{8}} = \square$
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the exponent - radical relationship

The formula for converting an expression with a fractional exponent to radical form is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), where \(n\) is the index of the radical and \(m\) is the power of the base \(a\). In the case of \(t^{\frac{1}{8}}\), we have \(a = t\), \(m=1\) and \(n = 8\).

Step2: Apply the formula

Using the formula \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), when \(a=t\), \(m = 1\) and \(n=8\), we substitute these values into the formula. So \(t^{\frac{1}{8}}=\sqrt[8]{t^{1}}\) or simply \(\sqrt[8]{t}\).

Answer:

\(\sqrt[8]{t}\)