which is an equivalent form of the expression 1800(1.2)^{-t}?\n1800(\\frac{1}{2})^{t}\n1800(\\frac{5}{6})^{t}…

which is an equivalent form of the expression 1800(1.2)^{-t}?\n1800(\\frac{1}{2})^{t}\n1800(\\frac{5}{6})^{t}\n1800(\\frac{6}{5})^{t}\n1800(\\frac{2}{1})^{t}

which is an equivalent form of the expression 1800(1.2)^{-t}?\n1800(\\frac{1}{2})^{t}\n1800(\\frac{5}{6})^{t}\n1800(\\frac{6}{5})^{t}\n1800(\\frac{2}{1})^{t}

Answer

Explanation:

Step1: Use negative - exponent rule

Recall the rule (a^{-n}=\frac{1}{a^{n}}). For the expression (1800(1.2)^{-t}), we can rewrite ((1.2)^{-t}) as (\frac{1}{(1.2)^{t}}). And (1.2=\frac{6}{5}), so ((1.2)^{-t}=(\frac{6}{5})^{-t}). By the negative - exponent rule (a^{-n}=\frac{1}{a^{n}}), ((\frac{6}{5})^{-t}=\left(\frac{5}{6}\right)^{t}). Then (1800(1.2)^{-t}=1800\left(\frac{5}{6}\right)^{t}).

Answer:

(1800\left(\frac{5}{6}\right)^{t}) (the second option)