Answer:
[tex]81x^4[/tex]
Step-by-step explanation:
Given: [tex]\sqrt[3]{(27x^3)^{4} }[/tex]
What we can do is rewrite the root as
[tex]\sqrt[3]{27x^3} ^4[/tex]
Then, calculate the cube root:
[tex]\sqrt[3]{27} = 3\\\sqrt[3]{x^3} =x[/tex]
We then get
[tex](3x)^4[/tex]
Distribute the fourth power into the expression
[tex](3)^4=81[/tex]
[tex](x)^4=x^4[/tex]
Final Answer
[tex]81x^4[/tex]
