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The order of operations is crucial in mathematics to ensure expressions are solved consistently and correctly. Often remembered by the acronym PEMDAS, it stands for:

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

Following this order helps to systematically solve mathematical expressions. When faced with a problem like \(6^{2} \cdot (10-8)\), you first address any operations inside parentheses, then calculate any exponents, followed by multiplication or division. This structured approach avoids mistakes and ensures everyone reaches the same solution.
Starting with parentheses means we simplify \(10 - 8\) to 2. This simplifies the problem and allows us to move on to the next step—exponents—without confusion.

Exponents are a shorthand way to show repeated multiplication of a number by itself. In the expression \(6^{2}\), the exponent "2" tells us to multiply the number 6 by itself once. So, \(6 \times 6\) equals 36. The base in this case is 6, and the exponent is 2.
This notion of multiplication being repeated is powerful as it greatly reduces long chains of multiplication into simpler, more compact expressions. Whenever you see an exponent, it requires evaluating it before moving on to multiplication or division (as per the order of operations).
Understanding exponents means recognizing that they dictate how many times to multiply the base by itself. This powerful operation makes calculations quicker and less cumbersome.

Multiplication is one of the core arithmetic operations and is essentially repeated addition. However, when it follows exponents in the order of operations, you need to multiply the resulting numbers. In our example, after evaluating the exponent, we are left with \(36 \cdot 2\).
To multiply 36 and 2, you add 36 two times:

• 1st 36 + 2nd 36 = 72

Alternatively, you could think about it as extending one number by a factor of the other. This attribute of multiplication as scaling up allows for flexibility in how teachers and learners view problems.
Always remember to perform multiplication after evaluating any exponents, as adhering to the order of operations ensures accurate, predictable outcomes.