please help... evaluate (27^1/9)^3
27
(27^(1/9))^3 = 27^(1/9 * 3) = 27^(1/3) = 3
To evaluate the expression (27^(1/9))^3, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break it down step by step:
Step 1: Evaluate the expression inside the parentheses.
27^(1/9) means taking the 9th root of 27. In other words, we need to find the number that, when raised to the power of 9, equals 27.
To evaluate it, we can rewrite 27 as 3^3 since 3^3 equals 27.
So, 27^(1/9) becomes (3^3)^(1/9). According to the properties of exponents, we can multiply the exponents: 3^(3 * 1/9).
The multiplication of 3 and 1/9 gives us 3/9 or 1/3. Therefore, the expression simplifies to 3^(1/3).
Step 2: Take the 3rd root of 3.
To evaluate 3^(1/3), you need to find the number that, when raised to the power of 3, equals 3.
The 3rd root of 3 is equal to 3 raised to the power of 1/3. Since the exponent 1/3 represents the 3rd root, we can leave it as it is.
So, (27^(1/9))^(3) simplifies to 3^(1/3)^(3).
Step 3: Evaluate the expression based on the exponent.
When we raise a number to a power and then raise that result to another power, we multiply the exponents. So, 3^(1/3)^(3) becomes 3^(1/3 * 3), which is equal to 3^(1) or simply 3.
Therefore, the answer is 3.
In summary, to evaluate the expression (27^(1/9))^3, we simplified it to 3^(1/3)^(3) and then used the exponent properties to solve it, resulting in the answer 3.