Question

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

Answer 1

Answer: Choice B

=========================================================

Step-by-step 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`