Question

Which radical expression in the picture is equivalent to t^5/8?

Answer 1

Answer: Choice B

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Explanation:

The rule we use is

$\Large a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$

where 'a' is the base, m stays in the role of the exponent, and n plays the role of the root index (eg: n = 3 is a cube root, n = 4 is a fourth root, and so on).

So for instance,

$\Large 2^{3/4} = \sqrt[4]{2^3} = \left(\sqrt[4]{2}\right)^3$

or in this case,

$\Large t^{5/8} = \sqrt[8]{t^5} = \left(\sqrt[8]{t}\right)^5$