Answer:
[tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex]
Step-by-step explanation:
We sure can write 2^2/5+ 3^1/10 as [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex]
// use the [tex]a^{\frac{m}{n} } =\sqrt[n]{a^{m} }[/tex] to transform the expression
Convert [tex]2^{\frac{2}{5} }[/tex] to [tex]\sqrt[5]{2^{2} }[/tex] = [tex]\sqrt[5]{4}[/tex] (here a = 2, n = 5, m = 2)
Then convert [tex]3^{\frac{1}{10} }[/tex] to [tex]\sqrt[10]{3^{1} }[/tex] = [tex]\sqrt[10]{3}[/tex] (here a = 3, n = 10, m = 1)
Now we get [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex] = [tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex] . This is the simplified form, which is the answer.
