Question

Find the value of the following expression:

(2^8 ⋅ 3^−5 ⋅ 6^0)^−2 ⋅ 3 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 2^28
Write your answer in simplified form. Show all of your steps.

Answer 1

Thank you, I was having a little bit of trouble with this, but then you helped.

Answer 2

`(2^8*3^(-5)*6^0)^(-2)*( \cfrac{3^(-2)}{2^3} )^4*2^(28)\\ \\\\ = (\cfrac{2^8}{3^5}*1)^(-2) *( \cfrac{1}{3^2*2^3} )^4*2^(28)\\\\\\=( \cfrac{3^5}{2^8} )^2* \cfrac{1^4}{3^(2*4)*2^(3*4)} *2^(28)\\\\\\= \cfrac{3^(5*2)}{2^(8*2)} * \cfrac{1}{3^8*2^(12)} *2^(28)\\\\\\=\cfrac{3^(10)}{2^(16)} * \cfrac{2^(28)}{3^8*2^(12)}\\\\\\= \cfrac{3^(10)*2^(28)}{3^8*2^(16+12)} \\\\\\=\cfrac{3^(10)*2^(28)}{3^8*2^(28)} \\\\=3^(10-8)*2^(28-28)\\\\=3^2*2^0\\\\=9*1\\\\=9`