%5E3-simplify.jpeg "(3^5)^3 Simplify")
Simplifying (3^5)^3
In mathematics, simplifying expressions involves rewriting them in a more concise and understandable form. Let's explore how to simplify the expression (3^5)^3.
Understanding the Power of a Power
The expression (3^5)^3 represents a power of a power. This means we have a base (3) raised to a power (5), and then that entire result is raised to another power (3).
To simplify this, we utilize the following rule:
(a^m)^n = a^(m*n)
Applying the Rule
- Identify the powers: We have m = 5 and n = 3.
- Multiply the powers: m * n = 5 * 3 = 15
- Rewrite the expression: (3^5)^3 = 3^(5*3) = 3^15
Final Simplified Form
Therefore, the simplified form of (3^5)^3 is 3^15.
This process demonstrates how to efficiently simplify expressions involving powers of powers by applying the appropriate mathematical rules.