%5E2-simplified.jpeg "(3x^3)^2 Simplified")
Simplifying (3x^3)^2
In mathematics, simplifying expressions is a crucial skill. Let's explore how to simplify the expression (3x^3)^2.
Understanding the Power of a Power
The expression involves two powers:
- (3x^3): This is a base (3x^3) raised to the power of 2.
- 2: This is the exponent, indicating that the base is multiplied by itself twice.
Applying the Power Rule
We can use the power of a power rule to simplify this expression. This rule states:
(a^m)^n = a^(m*n)
In our case, a is (3x^3), m is 3, and n is 2. Applying the rule, we get:
(3x^3)^2 = (3x^3)^(3 * 2) = (3x^3)^6
Simplifying Further
Now, we need to distribute the exponent 6 to both 3 and x^3:
(3x^3)^6 = 3^6 * (x^3)^6
Finally, calculate 3^6 and apply the power of a power rule again:
- 3^6 = 729
- (x^3)^6 = x^(3*6) = x^18
Therefore, the simplified expression is 729x^18.
Conclusion
By understanding the power of a power rule and applying it systematically, we can effectively simplify expressions involving exponents.