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Question 503861: please help me solve
[(5+3)^2/4]^2-3
Found 2 solutions by nerdybill, bucky:
Answer by nerdybill(7384)   (Show Source):
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! Given:
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Note that this is the way that your inline version of the problem translates to a different way of expressing it.
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Look first at the most interior set of parentheses. It contains 5+3, and this can be replaced by the sum 8. This replacement results in the expression becoming:
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Within the next higher set of parentheses, take care of the exponent first by squaring the 8 and getting 64. The expression then becomes:
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Next do the division within the parentheses. Divide 64 by 4 to get 16, and this gives:
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Then square the 16 to get 256 and the expression becomes:
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And finally do the subtraction to get the answer of 253.
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As a general rule follow the acronym PEMDAS meaning do Parentheses first, Exponents second, and then reading left to right do Multiplications and Divisions in the order that you encounter them, and as a last step do Additions and Subtractions as you encounter them. When you are working within a set of parentheses you follow the rules of EMDAS inside the parentheses to reduce the expression and then proceed to the next higher level of parentheses to apply a similar process until you reach the highest level.
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This process is why we looked for the most interior pair of parentheses first. It contained only 5 + 3, no exponents, multiplications, or divisions, only the one addition (that being 5 + 3) and no subtractions. So we did the addition.
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That left us inside the next higher level of parentheses with an exponent (squaring of 8), no multiplication, one division (divide by 4), and no additions or subtractions within that set of parentheses. The applicable order within the parentheses was to deal with the exponent first (square the 8 to get 64) and then to do the division by 4.
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Then the interior contents of the parentheses was down to 16. So the next action was to deal with the exponent for those contents (square the 16) and finally to do the last step ... the subtraction of 3.
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The point is that there is a logical order in which to do the PEMDAS steps that leads to a solution. With a little practice you will be able to see how to proceed with these steps.
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Hope this helps.
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