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Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Question about ex on pg 77
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At the top of page 77 in the book, there is an example for simplifying expressions containing rational exponents. The example includes five lines to complete the problem. The third line is: (x^2/3 * x^-1)(y*y^1/2). The next line goes to x^-1/3 y^3/2.
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I understand the problem and how they receive the numbers until they make the second to last step when they go from line three to line four. I do not understand where they get the negative 1/3 exponent for the variable x or where they get the 3/2 exponent for the variable y. Also, in the final step they switch the problem from multiplication to division..why? It goes from x^-1/3 y^3/2 to y^3/2 / x^1/3. I do not understand why it switches or why they get rid of the negative in the x^1/3.
Thank you!
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See if you can answer the questions below. You're welcome to submit your thinking and/or additional questions related to these questions:
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I'm going to assume that the expression is
(x^(2/3) * x^-1)(y*y^(1/2))
All those parentheses are necessary. As you wrote it the expression has a very different meaning, per the Typewriter Notation exercise. I do suggest that you enter your original expression in Wolfram Alpha and see how it is displayed.
In any case we have
(x^(2/3) * x^-1)(y*y^(1/2)).
What is x^(2/3) * x^(-1)?
What is y * y^(1/2)?
I'll put the answers to these questions below, but you'll want to try to answer them yourself in order to see why the expression does in fact become
x^(-1/3) y^(3/2)
(again note the need for those parentheses).
Now I believe the instructions for the problem asked you to express the final result with just positive exponents.
By the rule for negative exponents what does
x^(-1/3)
mean and how does that get you to the final result, which is
y^(3/2) / x^(1/3) ?
answers to posed questions:
x^a * x^b = x^(a + b) so
x^(2/3) * x^(-1) = x^(2/3 + (-1) ) = x^(-1/3).
and
y * y^(1/2) = y^1 * y^(1/2) = y^(1 + 1/2) = y^(3/2).
x^-a = 1 / x^a so
x^(-1/3) = 1 / x^(1/3).
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