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`