Need Help With Factoring Polynomials

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The expression (x^2)^3(2x^3)^3/(4x)^2 simplifies to (1/2)x^13. The numerator expands to 2x^15, while the denominator simplifies to 4x^2. By canceling the 4 with the 2 and applying exponent rules, two powers of x in the denominator are canceled from the numerator. This confirms that the final result is indeed (1/2)x^13. The calculations and reasoning provided validate the correctness of the solution.
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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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