Mathematics
Jesse777
2015-11-01 06:41:30
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.
ANSWERS
lazaro
2015-11-01 10:52:51

[latex](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[/latex]

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