[MOVED] simplify (x^-3 + y^-6)/(x^-6 y^2)
- Thread starter humakhan
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What is x<sup>-3</sup>, written with positive exponent?
What is y<sup>-6</sup>, written with positive exponent?
What is \(\displaystyle \frac{1}{x^3}\,+\,\frac{1}{y^6}\), written with a common denominator?
How do you simplify, when dividing by a fraction?
Please reply showing all the work you have done, including your answers to the above questions. Thank you.
Eliz.
What is y<sup>-6</sup>, written with positive exponent?
What is \(\displaystyle \frac{1}{x^3}\,+\,\frac{1}{y^6}\), written with a common denominator?
How do you simplify, when dividing by a fraction?
Please reply showing all the work you have done, including your answers to the above questions. Thank you.
Eliz.
http://www.algebrahelp.com/lessons/simp ... ac/pg3.htm
do teh same way as they did in this...
like
1
-------------------------
x^3 y^2 * x^3 + y^6
then
1
------------------------
x^9 y^8
right way or not?
do teh same way as they did in this...
like
1
-------------------------
x^3 y^2 * x^3 + y^6
then
1
------------------------
x^9 y^8
right way or not?
- Joined
- Feb 4, 2004
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The site in the link did not do what you did. If what you had done were correct, then the following sum:
. . . . .2<sup>-1</sup> + 3<sup>-1</sup> = 1/2 + 1/3
...would somehow "equal" 1/5 = 1/(2 + 3), and fractions simply don't work that way.
Instead, try following the instructions provided earlier: Write x<sup>-3</sup> and y<sup>-6</sup> as fractions with positive exponents. Convert them to a common denominator, and only then add them together. Then invert the fraction in the denominator, and multiply.
Eliz.
. . . . .2<sup>-1</sup> + 3<sup>-1</sup> = 1/2 + 1/3
...would somehow "equal" 1/5 = 1/(2 + 3), and fractions simply don't work that way.
Instead, try following the instructions provided earlier: Write x<sup>-3</sup> and y<sup>-6</sup> as fractions with positive exponents. Convert them to a common denominator, and only then add them together. Then invert the fraction in the denominator, and multiply.
Eliz.
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Okay, so you're doing the inversion first, instead of waiting to do that in the end. This will still work but, to count as being "simplified", you still need to do the other bits. You started with:humakhan said:
. . . . .\(\displaystyle \L \frac{x^{-3}\, +\, y^{-6}}{x^{-6}\, y^{2}}\)
You inverted first and multiplied:
. . . . .\(\displaystyle \L \left(x^{-3}\, +\, y^{-6}\right) \left(\frac{x^6}{y^2}\right)\)
Then you multiplied through, which simplifies as:
. . . . .\(\displaystyle \L \left(\frac{1}{x^3}\right)\left(\frac{x^6}{y^2}\right)\, +\, \left(\frac{1}{y^6}\right)\left(\frac{x^6}{y^2}\right)\)
. . . . .\(\displaystyle \L \frac{x^3}{y^2}\, +\, \frac{x^6}{y^8}\)
For some reason, you then re-factored, which is almost certainly not what your book wants. Instead, convert the two fractions to the common denominator of "y<sup>8</sup>", and combine into one fraction. This will give you the same answer as the step-by-step instructions that were provided earlier.
Eliz.