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

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

Answer 2

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