Question

2 to the power x - 1 / 2 to the power x + 1​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Simplify:

• $\dfrac{2^{x-1}}{2^{x+1}}$

Solution:

$:\implies \dfrac{2^{x-1}}{2^{x+1}} \\\\:\implies 2^{(x-1)-(x+1)} \\\\:\implies 2^{x-1-x-1} \\\\:\implies 2^{-2} \\\\:\implies \dfrac{1}{2^2} \\\\\bf{:\implies \dfrac{1}{4}}$

Formula used:

• $\dfrac{a^m}{a^n} = a^{m-n}$

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

Hope it helps..