The simplified radical expression for this problem is given by:
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
How to simplify the given radical expression?
To simplify the given radical expression, we divide all the exponents by 3, and the ones that can be simplified are placed outside the root, multiplying.
Looking at each term, we have that:
- 81 is equivalent to 3^4, hence [tex]\sqrt[3]{81} = \sqrt[3]{3^4} = 3\sqrt[3]{3}[/tex], as 4 divided by 3 has quotient 1 and remainder 1.
- For x^7, we have that 7 divided by 3 has quotient 2 and remainder 1, hence [tex]\sqrt[3]{x^7} = x^2\sqrt[3]{x}[/tex].
- For y^9, we have that 9 divided by 3 has quotient 3, hence [tex]\sqrt[3]{y^9} = y^3[/tex]
- For z^5, we have that 5 divided by 3 has quotient 1 and remainder 2, hence [tex]\sqrt[3]{z^5} = z\sqrt[3]{z^2}[/tex].
Thus, the simplified radical is given by:
[tex]3 \times \sqrt[3]{3} \times x^2 \times \sqrt[3]{x} \times y^3 \times z \times \sqrt[3]{z^2}[/tex]
[tex]3x^2y^3z\sqrt[3]{3xz^2}[/tex]
More can be learned about simplified radical expressions at https://brainly.com/question/738531
#SPJ1
