Respuesta :
To solve the problem we must know the basic exponential properties.
What are the basic exponent properties?
[tex]{a^m} \cdot {a^n} = a^{(m+n)}[/tex]
[tex]\dfrac{a^m}{a^n} = a^{(m-n)}[/tex]
[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]
[tex](a^m)^n = a^{m\times n}[/tex]
[tex](m\times n)^a = m^a\times n^a[/tex]
The expression can be written as [tex]x^9\sqrt[3]{y}[/tex].
Given to us
- [tex](x^{27}y)^\frac{1}{3}[/tex]
[tex](x^{27}y)^\frac{1}{3}[/tex]
Using the exponential property[tex](m\times n)^a = m^a\times n^a[/tex],
[tex]=(x^{27}y)^\frac{1}{3}\\\\=x^{\frac{27}{3}}\times y^\frac{1}{3}\\\\=x^9\times y^\frac{1}{3}[/tex]
Using the exponential property [tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex],
[tex]=x^9\times y^\frac{1}{3}\\\\=x^9\times \sqrt[3]{y}\\\\=x^9 \sqrt[3]{y}[/tex]
Hence, the expression can be written as [tex]x^9\sqrt[3]{y}[/tex].
Learn more about Exponent properties:
https://brainly.com/question/1807508
