%5E3-simplified.jpeg "(3^3)^3 Simplified")
(3^3)^3 Simplified: Unraveling the Complexity
Understanding Exponents
Before we dive into simplifying the expression (3^3)^3, it's essential to understand the concept of exponents. Exponents are mathematical notations that indicate the power to which a number should be raised. In the case of 3^3, the 3 is raised to the power of 3, meaning it is multiplied by itself three times.
The Original Expression
The expression (3^3)^3 can be broken down into two parts:
3^3is the inner expression, which equals 3 multiplied by itself three times, or3 × 3 × 3 = 27.- The outer expression is the result of the inner expression being raised to the power of 3, or
(27)^3.
Simplifying the Expression
To simplify (3^3)^3, we need to evaluate the inner expression first:
3^3 = 27 (as calculated earlier)
Now, we raise 27 to the power of 3:
(27)^3 = 27 × 27 × 27
Expanding the calculation, we get:
(27)^3 = 19683
Therefore, the simplified form of (3^3)^3 is:
(3^3)^3 = 19683
Conclusion
In conclusion, simplifying (3^3)^3 involves evaluating the inner expression 3^3 and then raising the result to the power of 3. By following the order of operations (PEMDAS), we arrive at the simplified answer of 19683.
