%5E3-simplified.jpeg "(5np^3)^3 Simplified")
Simplifying (5np^3)^3
When working with exponents, it's essential to understand the rules of exponentiation to simplify complex expressions. In this article, we'll break down the step-by-step process to simplify the expression (5np^3)^3.
Understanding Exponentiation Rules
Before we dive into the simplification process, let's quickly review the rules of exponentiation:
- Product of Powers: a^m * a^n = a^(m+n)
- Power of a Product: (ab)^m = a^m * b^m
- Power of a Power: (a^m)^n = a^(mn)
Simplifying (5np^3)^3
Now, let's apply these rules to simplify the given expression:
(5np^3)^3
Using the Power of a Product rule, we can expand the expression as:
(5^n * p^(3n))^3
Next, apply the Power of a Power rule to each factor:
= 5^(3n) * p^(3 * 3n) = 5^(3n) * p^(9n)
Final Simplification
To finalize the simplification, we can combine the exponents with the same base:
= 5^(3n) * p^(9n)
And that's it! We've successfully simplified the expression (5np^3)^3.
Remember, when working with exponents, it's crucial to apply the rules of exponentiation correctly to simplify complex expressions. Practice makes perfect, so try simplifying more expressions to master the rules!
