Final answer:
To simplify the expression (9²)¹/³, we square 9 to get 81 and then take the cube root of 81, which is 4.
Step-by-step explanation:
To simplify the expression (9²)¹/³, we use the properties of exponents. The expression means that we take the square of 9, which is 81, and then find the cube root of that result. So, we must raise 81 to the power of 1/3:
First, calculate 9²:
9² = 9 × 9 = 81
Then, find the cube root of 81 (which is 81¹/³):
81¹/³ = √³√81 = 4.32674871092 (approximation)
But we know that the exact cube root of 81 is 3, because 3³ = 27, so the next cube root we can think of, 4³, is 64, and after that is 5³ which is 125. Since 81 is between 64 and 125, the cube root of 81 is 4. Therefore, the simplified form of the expression is 4.