simplify 3^√54
note: you will find the option to add a cubic root symbol in the algebra (x) keyboard
To simplify 3^(√54), we need to find the value of √54 first.
√54 = √(9 * 6) = √9 * √6 = 3√6
Now we substitute this value back into the original expression:
3^(√54) = 3^(3√6)
Thus, the simplified expression is 3^(3√6).
To simplify 3^√54, we can rewrite it as (3^(1/3))^√(54) since the cube root and exponentiation are inverse operations.
Now let's simplify each part separately.
First, let's simplify the cube root of 54.
∛(54) is equal to 3 because 3^3 = 27 and 4^3 = 64, so the cube root of 54 lies between 3 and 4.
Now, let's simplify the exponentiation part.
(3^(1/3))^√(54) becomes (3^(1/3))^3 * 2.
Next, we can simplify the expression further.
3^(1/3)^3 can be written as 3^(1/3 * 3) which equals 3^1, resulting in just 3.
Therefore, 3^√54 simplifies to just 3.
To simplify the expression 3^(√54), we need to break it down step by step.
First, let's simplify the value inside the radical (√54):
1. √54 can be written as √(9 * 6).
2. Since 9 is a perfect square (3 * 3), we can take the square root of 9 outside the radical, giving us 3√6.
Now, our expression becomes 3^(3√6).
To simplify this further, we evaluate the expression inside the exponent (√6):
1. √6 is an irrational number, so we cannot simplify it further.
2. Instead, we leave it as √6.
Now, our final simplified expression is 3^(√6).