%5E2.jpeg "(a^3)^2")
(a^3)^2: Understanding Exponential Expressions
In mathematics, exponential expressions can often seem daunting, but breaking them down into simpler components can make them more manageable. One such expression is (a^3)^2, which may look complex at first, but can be easily evaluated by applying the rules of exponents.
What does the expression mean?
The expression (a^3)^2 is read as "a cubed to the power of 2" or "a to the power of 3, squared". It means we need to raise a to the power of 3, and then raise the result to the power of 2.
Evaluating the expression
To evaluate (a^3)^2, we can start by applying the rule of exponents that states:
a^(mn) = (a^m)^n
In our case, m = 3 and n = 2, so we can rewrite the expression as:
(a^3)^2 = a^(3*2) (a^3)^2 = a^6
This means that (a^3)^2 is equal to a raised to the power of 6.
Properties of Exponents
This example illustrates two important properties of exponents:
- Power of a Power: When we raise a power to another power, we multiply the exponents.
- Parentheses: When we have expressions inside parentheses, we evaluate them first before applying any other operations.
Conclusion
In conclusion, (a^3)^2 is equal to a^6, and evaluating this expression involves applying the rule of exponents and the properties of exponents. By breaking down complex expressions into simpler components, we can better understand the rules and properties that govern exponential expressions.
