Need Help With Factoring Polynomials

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    Factoring Polynomials
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Discussion Overview

The discussion revolves around the process of factoring polynomials, specifically focusing on the expression (x^2)^3(2x^3)^3/(4x)^2. Participants are examining the simplification of this expression and verifying the correctness of the resulting polynomial.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant claims to have simplified the expression to (1/2)x^13 and seeks confirmation of this result.
  • Another participant agrees with the initial claim, suggesting that the simplification is correct.
  • A third participant reiterates the original expression and confirms the result as (1/2)x^13, emphasizing clarity in notation.
  • A later reply provides a breakdown of the simplification process, explaining the cancellation of terms and the application of exponent rules, ultimately arriving at the same result of (1/2)x^13.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the simplification to (1/2)x^13, with no significant disagreement noted.

Contextual Notes

Some assumptions regarding the application of exponent rules and simplification steps are present, but these are not explicitly stated or resolved in the discussion.

Who May Find This Useful

Students or individuals seeking assistance with polynomial factoring and simplification techniques may find this discussion relevant.

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(x2)3(2x3)3/(4x)2

I got 1/2x^13, is this correct?
 
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I think so
 
REKLAW_WEHTTAM said:
(x2)3(2x3)3/(4x)2

I got 1/2x^13, is this correct?
For clarity use parentheses (1/2)x^13
 
Yeah, you've got it.
Remember that raising a power of ##x## to a power is like multiplying the exponents. So, ##(x^n)^m = x^{nm}##. In the numerator, you've got ##2x^{15}##, while in the denominator, you've got ##4x^2##. The 4 cancels the 2, and by basic exponent laws, the square in the denominator cancels two powers of ##x## in the numerator. So, you get ##\frac{1}{2} x^{13}##, which is what you got.
 

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