TenMarks teaches you how to simplify expressions with powers.
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Learn about Simplifying Powers In this lesson, let's learn how we simplify powers. We’ll try to do three problems where we have to simplify this. What this means is we take the number format, the value given to us in power and represent it in its true value. So let's do Part A first. Before we do, what is a power? Power is written as base with an exponent. The value here is BxBxB and we multiply it, exponent number of times. If this is four, we will see four Bs here. So let's try and solve the first one. It's is (-2)3, what that means is the base is -2 and I multiplied it by itself three times. So -2 x -2 is +4 and then +4 x -2 is -8; so, -23 = -8. A key thing to remember is -2 x -2 is +4, anytime you multiply two negatives, you get a positive. Let's try Part B. You got (2/3)2. What this means is 2/3 x 2/3 because the base is 2/3. This is the base and this is the exponent. So we multiply the base, exponent number of times. So in this case two times which gives me 2x2=4, 3x3=9. So 2/3 with an exponent of 2 is 4/9. Let's take some space and do the third one, which is -53. Notice here that negative is not within parenthesis with the five. So this is the same as -5 to the power or exponent three, or this could be -1 x 53 or 53. So this is -1, and what is five? The base is five and I have to multiply it three times, 5x5x5 is 125, 125 x -1 is negative 125. A key thing to remember is we always see what is the base. In this case, the base is five. The base is not -5. If the base was -5, it would have a parenthesis around it. But since we don’t have a parenthesis around it, the base is only 5 and that’s why five is the base that’s multiplied to itself three times and the negative sign remains outside.