Step-by-step explanation:
Given,
1. The given expression is [tex]\sqrt[10]{x^9}[/tex].
We need to write it into exponential form.
We know that,
[tex]\sqrt[a]{x} =x^{1/a}[/tex]
Here, a = 10
So,
[tex]\sqrt[10]{x^9}=(x^9)^{1/10}\\\\=x^{9\times \dfrac{1}{10}}\\\\=x^{9/10}\\\\=x^{0.1}[/tex]
2.
[tex](\sqrt[4]{3y} )^3\\\\=((3y)^3)^{1/4}\\\\=3^{3\times \dfrac{1}{4}}\times y^{3\times \dfrac{1}{4}}\\\\=3^{3/4}y^{3/4}[/tex]
Hence, this is the required solution.