How to Divide Power With Different Bases
A number raised to a power X equals that number multiplied by itself X -- 1 time. For example, you can evaluate 5 to the third power by multiplying 5 x 5 x 5 = 125. You can divide a number to one power by a second number to a different power by raising each number to the appropriate power and dividing the two results. But mathematicians like to do things in more elegant ways. In this case, you can determine how the two bases (the numbers being raised to powers) are related and evaluate the expression more easily.
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Instructions
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Write down the expression you want to evaluate. When dividing powers with different bases, the expression will have the form (A ** X)/(B ** Y), also written as A to the X power divided by B to the Y power. For example, say you want to determine (8 ** 5)/(6 ** 2), which is 8 to the fifth power divided by 6 to the second power.
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2
Divide B by A and call this number N. In the example, N = B/A = 0.75. This says that B = (0.75)(A).
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Raise A to the (X -- Y) power. In the example, X -- Y = 5 - 2 = 3, and 8 ** 3 = 512. Use a scientific calculator to check your work.
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Raise N to the Y power. In the example, (0.75) ** 2 = 0.5625. Compute this with your scientific calculator.
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Divide your answer from Step 3 by the answer in Step 4. In the example, 512/0.5625 = 910.22.
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Check your work by evaluating the expression the hard way. The numerator is 8 ** 5 = 32,768. The denominator is 6 ** 2 = 36. Divide the two to obtain 32,768/36 = 910.22.
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Tips & Warnings
In this article, we evaluated the expression (A ** X)/(B ** Y) by expressing it as (A ** X)/[(AN) ** Y], where B/A = N. We reduced this to [A ** (X -- Y)]/(N ** Y) and evaluated this instead of the original expression.
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