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a, =\(3^4+2^5=81+32=113\)
b, =\(3.\left(4^2-2.3\right)=3.\left(16-6\right)=3.10=30\)
c, =\(\dfrac{2^{12}.3^4.3^{10}}{2^{12}.3^{12}}=\dfrac{2^{12}.3^{14}}{2^{12}.3^{12}}=3^2=9\)
d, =\(\dfrac{3^2.7^2.2.7.5^3}{5^3.7^3.2.3}=3\)
e, =\(\dfrac{3^6.5^3.2^8.5^4.2^2.3^4}{2^{10}.3^{10}.5^5}=\dfrac{3^{10}.2^{10}.5^7}{2^{10}.3^{10}.5^5}=5^2=25\)
g, =\(\dfrac{2^5.\left(2^8+1\right)}{2^2.\left(2^8+1\right)}=\dfrac{2^5}{2^2}=2^3=8\)
\(b\)
\(\frac{2^{13+5}}{2^{10+2}}\)=\(\frac{2^{18}}{2^{12}}\)
\(a.\) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{2^3.3^3+3.3^2.2^2+3^3}{-13}=\frac{2^3.3^3+3^3.2^2+3^3}{-13}\)
\(=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=\frac{3^3.\left(-1\right)}{1}=-27\)
\(b.\)\(A=2^2+4^2+6^2+...+20^2=2^2\left(1+2^2+3^2+...+10^2\right)\)
\(A=2^2.\frac{10.\left(10+1\right).\left(2.10+1\right)}{6}=4.385=1540\)
( Ta có: công thức tính tổng bình phương liên tiếp tứ 1 đến n là: \(1^2+2^2+3^2+...+n^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\))
\(c.\)\(B=100^2+200^2+...+1000^2=\left(100.1\right)^2+\left(100.2\right)^2+...+\left(100.10\right)^2\)
\(B=100^2.1^2+100^2.2^2+...+100^2.10^2=100^2.\left(1^2+2^2+...+10^2\right)\)
Áp dụng công thức \(1^2+2^2+3^2+...+n^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\)
Ta có: \(B=100^2\times385=3,850,000\)
a/ 113
b/ 30
c/ 9
d/ 3
e/ 25
g/ 8
a)38:3^4+2^2.2^3=3^8-4+2^2+3=3^4+2^5=81+32=113
b)3.4^2-2.3^2=3(4^2-2.3)=3(16-6)=3.10=30
c)4^6.3^4.9^5/6^12=(2^2)^6.3^4.(3^2)^5/(2.3)^12=2^12.3^4.3^10/2^12.3^12=2^12.3^14/2^12.3^12=3^14/3^12=3^2=9
e)45^3.20^4.18^2/180^5=(5.3^2)^3.(2^2.5)^4.(2.3^2)^2/(2^2.3^2.5)^5=5^3.3^6.2^8.5^4.2^2.3^4/2^10.3^10.5^5=5^9.3^10.2^10/2^10.3^10.5^5
=5^4/1=5^4=625
d)21^2.14.125/35^3.6=(2.7)^2.2.7.5^3/(5.7)^3.2.3=2^2.7^2.2.7.5^3/5^3.7^3.2.3=2^3.7^3.5^3/5^3.7^3.2.3=2^3/2.3=8/6=4/3
g)2^13+2^5/2^10+2^2=2^5(2^8+1)/2^2(2^8+1)=2^5/2^2=32/4=8
Chúc bạn học tốt !!!!