Simplifying (5(8^(1/3)27^(1/3))^3)^(1/4):

To simplify this expression, we will follow the order of operations and apply the rules of exponents. Let's break down the steps:

Step 1: Simplify the expressions inside the parentheses
Step 2: Apply the exponent rule
Step 3: Evaluate the exponent outside the parentheses

Step 1: Simplify the expressions inside the parentheses

Inside the parentheses, we have 8^(1/3) and 27^(1/3). Let's simplify these individually:

- 8^(1/3):
The cube root of 8 is 2, because 2 * 2 * 2 = 8. Therefore, 8^(1/3) = 2.

- 27^(1/3):
The cube root of 27 is 3, because 3 * 3 * 3 = 27. Therefore, 27^(1/3) = 3.

Now, we substitute these values back into the expression:

5(2 * 3)^3

Step 2: Apply the exponent rule

We need to simplify (2 * 3)^3. According to the order of operations, we need to perform the multiplication before applying the exponent:

(2 * 3)^3 = 6^3

Now, we can evaluate 6^3:

5 * 6^3

Step 3: Evaluate the exponent outside the parentheses

Now, we have the expression 5 * 6^3. According to the order of operations, we need to simplify the exponent before performing the multiplication:

6^3 = 6 * 6 * 6 = 216

Now, we can evaluate the multiplication:

5 * 216 = 1080

Therefore, the simplified expression is 1080.

Final Answer:
(5(8^(1/3)27^(1/3))^3)^(1/4) simplifies to 1080.

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