## Is (5n)^2 = 5n^2?

This is a common misconception in algebra, but the equation **(5n)^2 = 5n^2** is **incorrect**. Let's break down why:

### Understanding Order of Operations

The order of operations (often remembered by the acronym PEMDAS or BODMAS) dictates the sequence in which we perform calculations:

**P**arentheses (or**B**rackets)**E**xponents (or**O**rders)**M**ultiplication and**D**ivision (from left to right)**A**ddition and**S**ubtraction (from left to right)

### Applying the Rules

Let's analyze both sides of the equation:

**(5n)^2:**This means we square the entire expression inside the parentheses. So, we first multiply 5n by itself: (5n) * (5n) = 25n^2**5n^2:**Here, we square only the variable 'n', then multiply by 5. This results in 5 * n * n = 5n^2

### The Difference

As we can see, **(5n)^2 = 25n^2** and **5n^2** are not equal. We need to follow the order of operations and square the entire expression in the parentheses for the left side of the equation.

### In Conclusion

The equation **(5n)^2 = 5n^2** is **incorrect**. Remember that squaring an expression inside parentheses applies to all elements within those parentheses, resulting in a different outcome than simply squaring the variable.