Question

Find the value of the following expression:

(2^8 ⋅ 3^−5 ⋅ 6^0)−2 * (3^-2 over 2^3)^4 * 2^28

Write your answer in simplified form. Show all of your steps

Answer 1

`image`

`\mathrm{Apply\:rule}\:a^0=1,\:a\\e \:0`

`6^0=1`

`=2^(28)\left((3^(-2))/(2^3)\right)^4\left(3^(-5)\cdot \:2^8\cdot \:1\right)^(-2)`

`\left(2^8\cdot \:3^(-5)\cdot \:1\right)^(-2)=\left(1\cdot (256)/(243)\right)^(-2)=\left((243)/(256)\right)^2`

`\left((3^(-2))/(2^3)\right)^4=(1^4)/(\left(2^3\cdot \:3^2\right)^4)=(1^4)/(3^8\cdot \:2^(12))`

`2^(28)\left((3^(-2))/(2^3)\right)^4\left(3^(-5)\cdot \:2^8\cdot \:1\right)^(-2)=(243^2\cdot \:1\cdot \:2^(28))/(256^2\cdot \:3^8\cdot \:2^(12))`

`=(2^(16)\cdot \:243^2)/(3^8\cdot \:256^2)`

`=(2^(16)\cdot \:3^(10))/(2^(16)\cdot \:3^8)`

`=3^2`

`=9`