Answer:
27
Step-by-step explanation:
[tex](\sqrt[4]{81})^3[/tex]
The rule to convert radical form into exponential form is
[tex](\sqrt[n]{x})^m = x ^\frac{m}{n}[/tex]
First we write the given radical form in exponential form
[tex](\sqrt[4]{81})^3=81^\frac{3}{4}[/tex]
81 = 3*3*3*3= 3^4
Replace 81 with 3^4
[tex](\sqrt[4]{81})^3=(3^4)^\frac{3}{4}[/tex]
Now we simplify the exponent, multiply 4 and 3/4
[tex](\sqrt[4]{81})^3=(3^4)^\frac{3}{4}= 3^3= 27[/tex]
