The discussion centers on the application of the laws of exponents, specifically the property that states \(a^m \cdot a^n = a^{m + n}\). The example provided illustrates this law using the expression \(2(2^{n + 1}) = 2^{n + 2}\), where \(2^1 \cdot 2^{n + 1} = 2^{1 + n + 1} = 2^{n + 2}\). Participants confirm that the leap made in the textbook is indeed valid according to this exponent rule.
PREREQUISITESStudents learning algebra, educators teaching exponent rules, and anyone seeking to strengthen their understanding of mathematical principles related to exponents.
tmt said:In my textbook,
it makes the leap from $2(2^{n + 1}) = 2^{n + 2}$ citing the laws of exponents.
I'm not sure which law of exponents it is referring to.
Thanks
Prove It said:$\displaystyle \begin{align*} a^m \cdot a^n = a^{m + n} \end{align*}$, and here you have $\displaystyle \begin{align*} 2^1 \cdot 2^{n + 1} = 2^{1 + n + 1} = 2^{n + 2} \end{align*}$.