Question

(2^8 * 3^-5 * 6^0)^-2 * (3^-2/ 2^3) ^4 * 2^28

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

Answer 1

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

`\left(2^8\cdot \:3^(-5)\cdot \:6^0\right)^(-2)\left((3^(-2))/(2^3)\right)^4\cdot \:2^(28)`

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

Consider

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

`=2^(28)\left((3^(-2))/(2^3)\right)^4(243^2)/(256^2)`

`=2^(28)\cdot (1)/(2^(12)\cdot \:3^8)\cdot (243^2)/(256^2)`

`=(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`