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\(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
Giải:
\(A_5=\left(-2x^2+x-5\right)+2x\left(x-1\right)-\left(x-5\right)\)
\(\Leftrightarrow A_5=-2x^2+x-5+2x^2-2x-x+5\)
\(\Leftrightarrow A_5=\left(-2x^2+2x^2\right)+\left(x-x\right)+\left(-5+5\right)-2x\)
\(\Leftrightarrow A_5=-2x\)
Vậy ...
\(A_6=-2x^2\left(2-3x\right)-3x\left(2x^2+x-1\right)\)
\(\Leftrightarrow A_6=-4x^2+6x^3-6x^3-3x^2+3x\)
\(\Leftrightarrow A_6=\left(-4x^2-3x^2\right)+\left(6x^3-6x^3\right)+3x\)
\(\Leftrightarrow A_6=-7x^2+3x\)
Vậy ...
C/MINH:
a.106 - 57 chia hết cho 59
Giải
ta có \(10^6-5^7=\left(2\cdot5\right)^6-5^7\)\(=2^6\cdot5^6-5^7=5^6\cdot\left(2^6-5\right)=5^6\cdot59⋮59\)
\(Q=2^3+4^3+...+20^3\)
\(Q=1^3.2^3+2^3.2^3+3^3.2^3+...+10^3.2^3\)
\(Q=\left(1^3+2^3+3^3+...+10^3\right).2^3\)
\(Q=3025.8\)
\(Q=24224\)
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{\left(2^2\right)^6.\left(3^2\right)^5+2^9.3^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\frac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)
\(=\frac{2.6}{3.5}=\frac{2.2}{1.5}=\frac{4}{5}\)
4^6.9^5+6^9.120/8^4.3^12-6^11
=2^12.3^10+2^9.3^9.2^3.3.5/2^12.3^12-6^11
=2^12.3^10+2^12.3^10.5/6^12-6^11
=2^13.3^10/6^11(6-1)
=2^13.3^10/6^11.5