a) 3^20/ 3^21 (3-1) = 3^20 / 3^21 * 2 = 1/ 2*3 = 1/6
b) 2^13*3^13/3^14 * 5^10/2^12*5^12= 2/3*5^10/5^12= 2/3*1/25= 2/75
c) 2^19*3^3*5^3*3^15/3^18*2^18*5^2= 2*3^3*5/3^3= 2*5=10
a) [tex]\frac{3^{20} }{3^{21}(3-1) }[/tex] = [tex]\frac{3^{20} }{3^{21}*2}[/tex]=[tex]\frac{1}{3*2}[/tex]=[tex]\frac{1}{6}[/tex]
b) [tex]\frac{2^{13} *3^{13} }{3^{14} }[/tex]*[tex]\frac{5^{10} }{2^{12}*5^{12} }[/tex]= [tex]\frac{2}{3}[/tex]*[tex]\frac{5^{10} }{5^{12} }[/tex]=[tex]\frac{2}{3}[/tex]*[tex]\frac{1}{25}[/tex]=[tex]\frac{2}{75}[/tex]
c) [tex]\frac{2^{19}*3^{3}*5^{3}*3^{15} }{3^{18} *2^{18}*5^{2} }[/tex]= [tex]\frac{2*3^{3}*5 }{3^{3} }[/tex]=2*5=10
[tex]a)\ \ \dfrac{3^2^0}{3^{22}-3^{21}}=\dfrac{3^2^0}{3\cdot3^2^1-3^2^1}=\dfrac{3^2^0}{(3-1)\cdot3^2^1}=\dfrac{\not3^2^0}{2\cdot3^2^1}=\dfrac{1}{2\cdot3^{21-20}}=\dfrac{1}{2\cdot3^1}=\\\\\\=\dfrac{1}{2\cdot3}=\dfrac{1}{6}\\\\\\b)\ \ \dfrac{6^1^3}{3^1^4}\cdot\dfrac{5^1^0}{10^1^2}=\dfrac{(2\cdot3)^1^3}{3^1^4}\cdot\dfrac{5^1^0}{(2\cdot5)^1^2}=\dfrac{2^1^3\cdot\not3^1^3}{3^1^4}\cdot\dfrac{\not5^1^0}{2^1^2\cdot5^1^2}=\dfrac{2^1^3}{3^{14-13}}\cdot\dfrac{1}{2^1^2\cdot5^{12-10}}=[/tex]
[tex]=\dfrac{2^1^3}{3^1}\cdot\dfrac{1}{2^1^2\cdot5^2}=\dfrac{2^1^3}{3}\cdot\dfrac{1}{\not2^1^2\cdot25}=\dfrac{2^{13-12}}{3}\cdot\dfrac{1}{25}=\dfrac{2^1}{3}\cdot\dfrac{1}{25}=\dfrac{2}{3}\cdot\dfrac{1}{25}=\dfrac{2}{75}[/tex]
[tex]c)\ \ \dfrac{2^1^9\cdot15^3\cdot3^1^5}{6^1^8\cdot5^2}=\dfrac{2^1^9\cdot(3\cdot5)^3\cdot3^1^5}{(3\cdot2)^{18}\cdot5^2}=\dfrac{2^1^9\cdot3^3\cdot5^3\cdot3^1^5}{3^1^8\cdot\not2^1^8\cdot\not5^2}=\dfrac{2^{19-18}\cdot3^3\cdot5^{3-2}\cdot3^1^5}{3^1^8}=\\\\\\=\dfrac{2^1\cdot3^{3+15}\cdot5^1}{3^1^8}=\dfrac{2\cdot\not3^1^8\cdot5}{\not3^1^8}=2\cdot5=10[/tex]
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Verified answer
a) 3^20/ 3^21 (3-1) = 3^20 / 3^21 * 2 = 1/ 2*3 = 1/6
b) 2^13*3^13/3^14 * 5^10/2^12*5^12= 2/3*5^10/5^12= 2/3*1/25= 2/75
c) 2^19*3^3*5^3*3^15/3^18*2^18*5^2= 2*3^3*5/3^3= 2*5=10
a) [tex]\frac{3^{20} }{3^{21}(3-1) }[/tex] = [tex]\frac{3^{20} }{3^{21}*2}[/tex]=[tex]\frac{1}{3*2}[/tex]=[tex]\frac{1}{6}[/tex]
b) [tex]\frac{2^{13} *3^{13} }{3^{14} }[/tex]*[tex]\frac{5^{10} }{2^{12}*5^{12} }[/tex]= [tex]\frac{2}{3}[/tex]*[tex]\frac{5^{10} }{5^{12} }[/tex]=[tex]\frac{2}{3}[/tex]*[tex]\frac{1}{25}[/tex]=[tex]\frac{2}{75}[/tex]
c) [tex]\frac{2^{19}*3^{3}*5^{3}*3^{15} }{3^{18} *2^{18}*5^{2} }[/tex]= [tex]\frac{2*3^{3}*5 }{3^{3} }[/tex]=2*5=10
[tex]a)\ \ \dfrac{3^2^0}{3^{22}-3^{21}}=\dfrac{3^2^0}{3\cdot3^2^1-3^2^1}=\dfrac{3^2^0}{(3-1)\cdot3^2^1}=\dfrac{\not3^2^0}{2\cdot3^2^1}=\dfrac{1}{2\cdot3^{21-20}}=\dfrac{1}{2\cdot3^1}=\\\\\\=\dfrac{1}{2\cdot3}=\dfrac{1}{6}\\\\\\b)\ \ \dfrac{6^1^3}{3^1^4}\cdot\dfrac{5^1^0}{10^1^2}=\dfrac{(2\cdot3)^1^3}{3^1^4}\cdot\dfrac{5^1^0}{(2\cdot5)^1^2}=\dfrac{2^1^3\cdot\not3^1^3}{3^1^4}\cdot\dfrac{\not5^1^0}{2^1^2\cdot5^1^2}=\dfrac{2^1^3}{3^{14-13}}\cdot\dfrac{1}{2^1^2\cdot5^{12-10}}=[/tex]
[tex]=\dfrac{2^1^3}{3^1}\cdot\dfrac{1}{2^1^2\cdot5^2}=\dfrac{2^1^3}{3}\cdot\dfrac{1}{\not2^1^2\cdot25}=\dfrac{2^{13-12}}{3}\cdot\dfrac{1}{25}=\dfrac{2^1}{3}\cdot\dfrac{1}{25}=\dfrac{2}{3}\cdot\dfrac{1}{25}=\dfrac{2}{75}[/tex]
[tex]c)\ \ \dfrac{2^1^9\cdot15^3\cdot3^1^5}{6^1^8\cdot5^2}=\dfrac{2^1^9\cdot(3\cdot5)^3\cdot3^1^5}{(3\cdot2)^{18}\cdot5^2}=\dfrac{2^1^9\cdot3^3\cdot5^3\cdot3^1^5}{3^1^8\cdot\not2^1^8\cdot\not5^2}=\dfrac{2^{19-18}\cdot3^3\cdot5^{3-2}\cdot3^1^5}{3^1^8}=\\\\\\=\dfrac{2^1\cdot3^{3+15}\cdot5^1}{3^1^8}=\dfrac{2\cdot\not3^1^8\cdot5}{\not3^1^8}=2\cdot5=10[/tex]