%5E3.jpeg "(3a^2)^3")
Simplifying (3a^2)^3
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves expressions with exponents. Let's break down how to simplify the expression (3a^2)^3.
Understanding the Power of a Power
The expression (3a^2)^3 represents (3a^2) multiplied by itself three times:
(3a^2)^3 = (3a^2) * (3a^2) * (3a^2)
Applying the Power Rule
To simplify this, we use the power of a power rule, which states that (x^m)^n = x^(m*n).
In our expression, x = 3a^2, m = 2, and n = 3. Applying the rule, we get:
(3a^2)^3 = 3^(23) * a^(23)
Final Simplification
Simplifying the exponents, we arrive at:
(3a^2)^3 = 3^6 * a^6
Finally, calculating 3^6, we obtain:
**(3a^2)^3 = ** 729a^6
Conclusion
Therefore, the simplified form of (3a^2)^3 is 729a^6. This process illustrates the importance of understanding exponent rules and applying them systematically to simplify expressions.