%5E3-simplified.jpeg "(3a^2)^3 Simplified")
Simplifying (3a^2)^3
In algebra, simplifying expressions is an essential skill to master. One such expression that may seem daunting is (3a^2)^3. However, with the correct application of exponent rules, we can simplify this expression to a more manageable form.
Breaking Down the Expression
Let's break down the expression (3a^2)^3:
- We have a expression inside the parentheses, which is 3a^2.
- This expression is raised to the power of 3.
Applying Exponent Rules
To simplify this expression, we need to apply the exponent rule that states:
(ab)^n = a^n * b^n
In our case, a = 3, b = a^2, and n = 3. Substituting these values, we get:
(3a^2)^3 = 3^3 * (a^2)^3
Simplifying the Expression
Now, we can simplify each part of the expression:
- 3^3 = 27 (since 3 to the power of 3 is 27)
- (a^2)^3 = a^(2*3) = a^6 (using the exponent rule that states (a^m)^n = a^(m*n))
Substituting these values, we get:
(3a^2)^3 = 27a^6
And that's the simplified form of the expression!
Conclusion
In conclusion, simplifying (3a^2)^3 requires the application of the correct exponent rules. By breaking down the expression and applying the rules, we can simplify it to 27a^6. This skill is essential in algebra and will help you tackle more complex expressions with ease.
