Question

PLEASE HELP! I DON'T UNDERSTAND!! SOMEONE SMART HELP!!!

Find the value of the following expression:

(38 ⋅ 2−5 ⋅ 90)−2 ⋅ 2 to the power of negative 2 over 3 to the power of 3, whole to the power of 4 ⋅ 328 (5 points)

Write your answer in simplified form. Show all of your steps. (5 points)

Answer 1

$\bf \left( 3^8\cdot 2^{-5}\cdot 9^0 \right)^{-2}\cdot \left( \cfrac{2^{-2}}{3^3} \right)^4\cdot 3^{28} \\\\\\ \left( 3^8\cdot 2^{-5}\cdot 1 \right)^{-2}\cdot \left( \cfrac{2^{-2}}{3^3} \right)^4\cdot 3^{28}\implies \left( 3^8\cdot 2^{-5}\right)^{-2}\cdot \left( \cfrac{2^{-2}}{3^3} \right)^4\cdot 3^{28}$

$\bf \stackrel{\textit{distributing the exponents}}{\left( 3^{-2\cdot 8}\cdot 2^{-2\cdot -5} \right)\cdot \left( \cfrac{2^{4\cdot -2}}{3^{4\cdot 3}} \right)\cdot 3^{28}}\implies \left( 3^{-16}\cdot 2^{10} \right)\cdot \left( \cfrac{2^{-8}}{3^{12}} \right)\cdot 3^{28}$

$\bf \cfrac{3^{-16}\cdot 2^{10}\cdot 2^{-8}\cdot 3^{28}}{3^{12}}\implies \cfrac{3^{-16}\cdot 3^{28}\cdot 2^{10}\cdot 2^{-8}}{3^{12}} \\\\\\ \cfrac{3^{-16+28}\cdot 2^{10-8}}{3^{12}}\implies \cfrac{\underline{3^{12}}\cdot 2^2}{\underline{3^{12}}}\implies 2^2\implies 4$