Simply math question, lets say I have $(2x^2)^3$.Is this equal to $8x^6 , 2x^5, 2x^6$, or $8x^5$ ? It is a simple problem but what confuses me is do if I multiply the coefficient separately from the variable such as $(2^3 * (x^2)^3)$? then I don't understand when to add the exponents with one another and when you multiply them?

Thank you

  • $\begingroup$ Your are correct (first answer). $(ab)^3=(a)^3(b)^3$ with $a=2$ and $b=x^3$. You add exponents when you have the same base: $a^3*a^3=a^6$. If you have different bases, nothing can be done, e.g. $x^3y^3$ cannot be simplified. You multiply exponents when you raise an exponential to another power: $(a^3)^3=a^9$. $\endgroup$
    – David P
    Feb 19 '14 at 3:24
  • $\begingroup$ @DavidPeterson $2^3\cdot5^3=10^3$. $\endgroup$ Feb 19 '14 at 7:10

Rather than give you the answer, let me show the work $$ (2 X^2)^3 = (2 X^2)\times (2 X^2) \times (2 X^2) = 2 \times 2 \times 2 \times X^2\times X^2\times X^2= 8 X^6$$

Hope this helps you in not only knowing what the answer is but also why it is the answer.

  • $\begingroup$ Yes thank you for explaining why it works, I'm a junior in high school taking an algebra 2 course will move onto pre-calculus next year and I didn't know the difference. This is my major concern with the school system as teachers presents a concept and how to solve problems but never explain WHY its works.. $\endgroup$
    – AlanZ2223
    Feb 19 '14 at 3:32
  • $\begingroup$ It is nice to see juniors here. We are all here to help. $\endgroup$
    – user44197
    Feb 19 '14 at 3:35

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