Question

Can you please simplify these expressions in two forms: radical and simplified without exponents?

I don't really understand how fractional exponents work, so an explanation would be appreciated.
27^4/3
36^3/2
(1/8)^2/3
128^5/7
Thank you :)

Answer 1

(a.) 27^4/3 = 81, (b.) 36^3/2 = 216, (c.) (1/8)^2/3 = 1/4, (d.) 128^5/7 = 32

Explanation:

All these expressions can be converted in square roots.

In order to do this, we can picture the fractional exponents as exponent / index

(a.) So for this first problem, we would have the cube root of
`27^{(4)/(3) }` or

`\sqrt[3]{(27)^(4) }`.

We must do the equation inside the radical first (i.e.,
`(27)^(4)`) to get
`\sqrt[3]{531,441}` = 81

We can follow these same steps for the remaining equations:

(b.)
`36^{(3)/(2) }` =
`√((36)^3)` =
`√(46,656)` = 216

(c.)
`((1)/(8))^(2)/(3)` =
`\sqrt[3]{((1)/(8))^(2) }` =
`\sqrt[3]{((1^2)/(8^2)) }` =
`\sqrt[3]{((1)/(64)) }` =
`(1)/(4)`

(d.)
`128^{(5)/(7) }` =
`\sqrt[7]{(128)^(5) }` = 32