![]() ![]() Let us summarize these findings in a table.Įxample 2: Evaluating Powers with Negative ExponentsĮvaluate the following expression: 6 ⋅ 2 . If we carry out the division by 7 once more, we get So, we start seeing a pattern here: every time we divide by 7, the exponent decreases by 1. The number 7 is of course simply 7, but it is useful to write the exponent here, as you will see in the If we perform the same division again on 7 , we get Let us look at what happens when we divide the power of a number by this number, for instance, 7 divided by 7. To understand the meaning of extending the exponents to negative numbers, So far, we have assumed that the exponent is positive. The question now is whether we could express the result of the previous question, 1 7, as a power of 7. So, here, the eleven 7s in the numerator cancel out withĮleven out of the twelve 7s in the denominator to give 1. Now, we know that one 7 in the numerator cancels out with one 7 in the denominator sinceħ 7 = 1. We have already simplified our expression to Similarly, we find that theĭenominator is 7 . ![]() This is the product rule, which states that The factor 7 and that the factor 7 would appear 3 + 2 + 6 = 1 1 times. By expandingĪll the powers, we see that the numerator would consist of a repeated multiplication of We notice that in this expression, all the powers have the same base: 7. Example 1: Quotient of Powers of the Same Base ![]()
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