a)[tex]32^2*2^7=(2^5)^2*2^7=2^{10}*2^7=2^{17}[/tex]
b) [tex]125^4:25^4=(5^3)^4:(5^2)^4=5^{12}:5^8=5^4[/tex]
[tex]c) (3*9^5):(27^2*9)\\3*(3^2)^5=3*3^{10}=3^{11}\\(3^3)^2*3^2=3^6*3^2=3^8\\3^{11}:3^8=3^3[/tex]
[tex]d) (\frac{1}{3})^2*(\frac{1}{9})^3:\frac{1}{27} =(\frac{1}{3})^2*((\frac{1}{3})^2)^2:(\frac{1}{3})^3=(\frac{1}{3})^2*(\frac{1}{3})^4:(\frac{1}{3})^3=(\frac{1}{3})^3[/tex]
[tex]e) 3*2^4+4^2=3*2^4+(2^2)^2=3*2^4+2^4=3*2*2^4=3*2^5[/tex]
[tex]f) 7*5^6-2*25^3=7*5^6-2*(5^2)^3=7*5^6-2*5^6=5*5^6=5^7[/tex]
[tex]g) \frac{(2^3)^2*3^3+15*3^2-5*27}{3^3*2}=\frac{2^6*3^3+5*3*3^2-5*3^3}{3^3*2} =\frac{2^6*3^3+5*3^3-5*3^3}{3^3*2} =\frac{2^6*3^3}{2*3^3}=2^5[/tex]
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a)[tex]32^2*2^7=(2^5)^2*2^7=2^{10}*2^7=2^{17}[/tex]
b) [tex]125^4:25^4=(5^3)^4:(5^2)^4=5^{12}:5^8=5^4[/tex]
[tex]c) (3*9^5):(27^2*9)\\3*(3^2)^5=3*3^{10}=3^{11}\\(3^3)^2*3^2=3^6*3^2=3^8\\3^{11}:3^8=3^3[/tex]
[tex]d) (\frac{1}{3})^2*(\frac{1}{9})^3:\frac{1}{27} =(\frac{1}{3})^2*((\frac{1}{3})^2)^2:(\frac{1}{3})^3=(\frac{1}{3})^2*(\frac{1}{3})^4:(\frac{1}{3})^3=(\frac{1}{3})^3[/tex]
[tex]e) 3*2^4+4^2=3*2^4+(2^2)^2=3*2^4+2^4=3*2*2^4=3*2^5[/tex]
[tex]f) 7*5^6-2*25^3=7*5^6-2*(5^2)^3=7*5^6-2*5^6=5*5^6=5^7[/tex]
[tex]g) \frac{(2^3)^2*3^3+15*3^2-5*27}{3^3*2}=\frac{2^6*3^3+5*3*3^2-5*3^3}{3^3*2} =\frac{2^6*3^3+5*3^3-5*3^3}{3^3*2} =\frac{2^6*3^3}{2*3^3}=2^5[/tex]