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# Exponents & The Order of Operations

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In this lesson, we will review the basic definition of an exponent. Recall that at the most basic level, an exponent allows us to write repeated multiplication of the same number more conveniently. For example, we could write: 4 • 4 • 4 • 4 • 4 = 45. The larger number (4) is known as the base. The base is the number that is involved in the repeated multiplication. The smaller number at the top right is known as the exponent. The exponent tells us how many factors of the base are present in the repeated multiplication. Additionally, we will review how to work with exponents with a negative base. This is a topic that commonly trips students up. Suppose we consider a scenario such as: (-5)2 = +25, the answer is different vs: -52 = -25. The reason is simple; we must include the negative sign inside of the parentheses for it to be raised to the given power. Lastly, we will review the order of operations, which is commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiply/Divide, Addition/Subtraction). The order of operations tells us which operation to perform in which order when faced with multiple operations in a problem. We always begin with parentheses or any grouping symbols that are present. Secondly, we apply any exponents or perform any radical operations. For the third step, we multiply or divide moving from left to right. This is a common source of confusion because of the PEMDAS acronym. The MD stands for multiply or divide from left to right, but since the M is placed before the D, most students interpret this to mean that they should multiply before they divide. For the fourth and final step, we add or subtract, again moving from left to right. Once more, the AD in PEMDAS often causes confusion on this step as well.
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