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\(a,3^{n+2}-3^{n+1}+6.3^n\)
\(=3^n\left(3^2-3+6\right)=3^n.12\)
\(b,\left(3.2^{n+2}+2^n+2^{n+1}\right):5\)
\(=\left[2^n\left(3.2^2+1+2\right)\right]:5\)
\(=2^n.15:5\)
\(=2^n.3\)
a) \(3^n+3^{n+2}=3^n.\left(1+3^2\right)=3^n.\left(1+9\right)=10.3^n\)
b) \(1,5.2^n-2^{n-1}=1,5.2^{1+n-1}-2^{n-1}=1,5.2.2^{n-1}-2^{n-1}\)
\(=3.2^{n-1}-2^{n-1}=2^{n-1}.\left(3-1\right)=2^{n-1}.2=2^n\)
\(a,9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^{\left(-4\right)}.3^2=3^{2+3-4+2}=3^3.\)
\(b,4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.2^{-4}\right)=2^{2+5}:2^{3-4}=2^7:2^{-1}=2^{7-\left(-1\right)}=2^8.\)
\(c,3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=\left(\frac{3^2}{3^2}\right).\left(2^5.2^2\right)=1.2^{5+2}=2^7\)
\(d,\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^2.\frac{1}{3}.\left(3^2\right)^2=\left(\frac{1}{3}\right)^{2+1}.3^4=\left(\frac{1}{3}\right)^3.\left(\frac{1}{3}\right)^{-4}=\left(\frac{1}{3}\right)^{3-4}=\left(\frac{1}{3}\right)^{-1}=3^1\)
a) \(10^n+1-6\cdot10^n=\left(1-6\right)10^n+1=-5\cdot10^n+1\)
b) \(90\cdot10^n-10^2-2+10^n+1=\left(90-1+1\right)\cdot10^n-2+1=90\cdot10^n-1\)
c) \(2,5\cdot56^n-3=\frac{5}{2}\cdot56^n-3\)
3^(n+2) - 3^(n+1)-6x3^n= 3^n x 3^2 - 3^n x 3 - 6x3^n = 3^n x (3-2+6) =3^n x 7 ( câu b tương tự )