MHB Simplification of Expressions with Exponents

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To simplify expressions with exponents without a calculator, understanding the Laws of Exponents is essential. Participants in the discussion emphasize the importance of applying these laws to evaluate expressions accurately. The conversation encourages sharing methods and techniques used for simplification. Users are prompted to discuss their attempts and strategies for solving the problems presented. Mastery of these concepts allows for effective evaluation of exponential expressions.
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Evaluate each of the following without using the calculator.

View attachment 468

View attachment 469

how to evaluate without even using calculator?
 

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thorpelizts said:
Evaluate each of the following without using the calculator.

https://www.physicsforums.com/attachments/468

View attachment 469

how to evaluate without even using calculator?

Hi thorpelizts, :)

All you need to know to simplify these expressions are the Laws of Exponents. What have you tried so far?
 

Thread 'Significant figures for inherently bound values'

I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
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