91Ó°ÊÓ

The order of operations is crucial when solving mathematical expressions, especially when they involve multiple steps like parentheses, exponents, and basic arithmetic operations. Remember the acronym PEMDAS to help you remember the order:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order ensures that everyone solves mathematical expressions the same way, achieving the same result. In our exercise, we start by handling what's inside the parentheses first: subtracting \(\frac{2}{5}\) from 1. Once simplified, we deal with the exponent next.

Arithmetic operations are the building blocks of math and include addition, subtraction, multiplication, and division. When you're dealing with fractions, these operations can sometimes seem tricky, but understanding how to manipulate fractions makes it much simpler.
In the problem, we subtract fractions. To do this correctly, it's important to have a common denominator. Here, the common denominator is 5. We rewrite 1 as \(\frac{5}{5}\), making it easier to subtract \(\frac{2}{5}\). This operation is essential in simplifying the expression within the parentheses before moving on to other steps.
Once we understand how to add and subtract fractions, handling whole numbers as fractions becomes more intuitive and helps in other operations too.

Exponentiation is the process of raising a number to a certain power. It's like multiplying the number by itself a number of times. In our exercise, we have to square a fraction, \(\left(\frac{3}{5}\right)^2\).
To square a fraction, you independently square the numerator and the denominator. Here, \(3^2 = 9\) and \(5^2 = 25\). So squaring \(\frac{3}{5}\) gives us \(\frac{9}{25}\).
Understanding exponentiation is vital in mathematics. It allows us to greatly simplify expressions and solve equations efficiently, especially when dealing with powers and roots.