Question

Simplify the express to demonstrate the power of a power prope

that demonstrate how you arrived at the simplified answer.
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Answer 1

The simplest form is
`3^{(1)/(2)}`

Explanation:

* Lets explain some rules in the power

-
`a^(m)*a^(n)=a^(m+n)`

# Ex: 5² × 5³ = 5^5 because with the same bases we add the powers

∵ 5² = 5 × 5 and 5³ = 5 × 5 × 5

∴ 5² × 5³ = 5 × 5 × 5 × 5 × 5 = 5^5

-
`(a^(m))^(n)=a^(mn)`

# Ex:
`(3^(2))^(3)=3^(2*3)=3^(6)` because we multiply powers

∵ 3² = 3 × 3 and (3²)³ = 3² × 3² × 3² by using the rule above we will

add the powers

∴ (3²)³ = 3^6

* Lets solve the problem

∵
`(3^{(1)/(4)})^(2)=(3^{(1)/(4)})*(3^{(1)/(4)})`

- The bases are same so we will add the powers

∴
`(3^{(1)/(4)})*(3^{(1)/(4)})=3^{(1)/(4)+(1)/(4)}=3^{(2)/(4)}=3^{(1)/(2)}`

∴ The simplest form of
`(3^{(1)/(4)})^(2)` is
`3^{(1)/(2)}`