%5E2-answer.jpeg "(a^3)^2 Answer")
Exponent Rules: Simplifying (a^3)^2
When working with exponents, it's essential to understand the rules and properties that govern them. In this article, we'll explore the exponent rule that helps us simplify expressions like (a^3)^2.
The Power of a Power Rule
The power of a power rule states that when you raise a power to another power, you multiply the exponents. Mathematically, this can be represented as:
(a^m)^n = a^(mn)
Where 'm' and 'n' are integers, and 'a' is a real number.
Simplifying (a^3)^2
Now, let's apply this rule to simplify the expression (a^3)^2:
(a^3)^2 = a^(3*2) (a^3)^2 = a^6
As you can see, by applying the power of a power rule, we can simplify the expression (a^3)^2 to a^6.
Why Does This Rule Work?
To understand why this rule works, let's think about what each exponent represents. The exponent '3' in a^3 represents three instances of 'a' multiplied together:
a^3 = aaa
Now, when we raise this to the power of 2, we're essentially multiplying three instances of 'a' together twice:
(a^3)^2 = (aaa)^2 (a^3)^2 = (aaa)(aa*a) (a^3)^2 = aaaaa*a
Simplifying this expression, we get:
(a^3)^2 = a^6
This demonstrates why the power of a power rule works: it allows us to simplify complex exponent expressions by multiplying the exponents together.
Conclusion
In conclusion, the power of a power rule is a powerful tool for simplifying exponent expressions. By understanding this rule, we can simplify complex expressions like (a^3)^2 to their simplest form. Remember, when you raise a power to another power, you multiply the exponents!
