Need Help With Factoring Polynomials

[REKLAW_WEHTTAM]

(x²)³(2x³)³/(4x)²

I got 1/2x^13, is this correct?

 

[Maged Saeed]

I think so

 

[mathman]

(x²)³(2x³)³/(4x)²

I got 1/2x^13, is this correct?

For clarity use parentheses (1/2)x^13

 

[AMenendez]

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.

 

[CellCoree]

Hello! Thank you for reaching out for help with factoring polynomials. Unfortunately, the answer you provided is not correct. Let's go through the steps together to find the correct solution.

First, let's simplify the given expression: (x^2)^3(2x^3)^3/(4x)^2. We can use the power rule to simplify the exponents: x^6(8x^9)/16x^2.

Next, we can combine like terms by dividing the coefficients and subtracting the exponents: (8/16)x^(9-2+6) = (1/2)x^13. Therefore, the correct solution is (1/2)x^13.

I hope this helps! Remember to always check your answers by distributing the factored expression to ensure it simplifies back to the original expression. Keep practicing and you will become a pro at factoring polynomials. Good luck!