Question

What is the radical form of each of the given expressions?

Drag the answer into the box to match each expression.

Choices in photo below.

Answer 1

Answer:
`5^{(2)/(3)}= \sqrt[3]{5^2}`

`5^{(1)/(2)}= √(5)`

`3^{(2)/(5)}= \sqrt[5]{3^2}`

`3^{(5)/(2)}= √(3^5)`

Step-by-step explanation: According to the rule of exponent of radical form:

`a^{(m)/(n) } = \sqrt[n]{a^m}`.

Let us apply same rule in first number

`5^{(2)/(3)}= \sqrt[3]{5^2}`

`5^{(1)/(2)}= √(5)`

`3^{(2)/(5)}= \sqrt[5]{3^2}`

`3^{(5)/(2)}= √(3^5)`

Note: When we don't have any number on the top of radical, there 2 is understood.

Answer 2

The main rule to apply here is:

(i)
`\displaystyle{ a^ {\displaystyle{ ((b)/(c))} }= \displaystyle{ \sqrt[c]{a^b}`

(ii)If c=2, then we write the following
`\displaystyle{ a^ {\displaystyle{ ((b)/(2))} }= \displaystyle{ √(a^b)`.


According to these rules:


`\displaystyle{ 5^ {\displaystyle{ ((2)/(3))} }= \displaystyle{ \sqrt[3]{5^2}`.


`\displaystyle{ 5^ {\displaystyle{ ((1)/(2))} }= \displaystyle{ √(5^1)=\displaystyle{ √(5)`.


`\displaystyle{ 3^ {\displaystyle{ ((2)/(5))} }= \displaystyle{ \sqrt[5]{3^2}`.


`\displaystyle{ 3^ {\displaystyle{ ((5)/(2))} }= \displaystyle{ √(3^5)`.