# Problem with raising parentheses to powers

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

• 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: $(a^3)^3=a^9$. Feb 19 '14 at 3:24
• @DavidPeterson $2^3\cdot5^3=10^3$. Feb 19 '14 at 7:10

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