%5E2.jpeg "(6a^5)^2")
Simplifying (6a^5)^2
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (6a^5)^2.
Understanding the Power of a Power
The expression (6a^5)^2 represents the square of the entire term inside the parentheses. This means we are multiplying the term (6a^5) by itself.
Applying the Power of a Product Rule
We can simplify this using the power of a product rule: (ab)^n = a^n * b^n
Applying this rule, we get:
(6a^5)^2 = 6^2 * (a^5)^2
Simplifying Further
Now, we need to apply the power of a power rule: (a^m)^n = a^(m*n)
Using this, we can simplify the expression:
6^2 * (a^5)^2 = 36 * a^(5*2)
This simplifies to:
36a^10
Conclusion
Therefore, the simplified form of (6a^5)^2 is 36a^10. Remember, understanding the rules of exponents is key to simplifying complex expressions.