Answer:
The simplest form is [tex]3^{\frac{1}{2}}[/tex]
Step-by-step explanation:
* Lets explain some rules in the power
- [tex]a^{m}*a^{n}=a^{m+n}[/tex]
# 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
- [tex](a^{m})^{n}=a^{mn}[/tex]
# Ex: [tex](3^{2})^{3}=3^{2*3}=3^{6}[/tex] 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
∵ [tex](3^{\frac{1}{4}})^{2}=(3^{\frac{1}{4}})*(3^{\frac{1}{4}})[/tex]
- The bases are same so we will add the powers
∴ [tex](3^{\frac{1}{4}})*(3^{\frac{1}{4}})=3^{\frac{1}{4}+\frac{1}{4}}=3^{\frac{2}{4}}=3^{\frac{1}{2}}[/tex]
∴ The simplest form of [tex](3^{\frac{1}{4}})^{2}[/tex] is [tex]3^{\frac{1}{2}}[/tex]
