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a: \(=2^6\cdot2^{20}=2^{26}\)
b: \(=3^9\cdot3^8\cdot3^2\cdot2\cdot13=3^{19}\cdot2\cdot13\)
a: \(=\left(\dfrac{-48}{12}+\dfrac{-8}{12}+\dfrac{21}{12}\right)\cdot\dfrac{-12}{13}\)
\(=\dfrac{-35}{12}\cdot\dfrac{-12}{13}=\dfrac{35}{13}\)
b: \(=\dfrac{-3}{6}+\dfrac{5}{6}-\dfrac{312}{100}+\dfrac{51}{10}\)
\(=\dfrac{1}{3}-\dfrac{312}{100}+\dfrac{51}{10}=\dfrac{347}{150}\)
c: \(=\left(\dfrac{48}{300}+\dfrac{175}{300}-\dfrac{135}{100}\right)\cdot\dfrac{5}{2}+\dfrac{1}{4}\)
\(=\dfrac{88}{300}\cdot\dfrac{5}{2}+\dfrac{1}{4}=\dfrac{59}{60}\)
Rút gọn các biểu thức sau:
E = \(\dfrac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\dfrac{3^2\cdot5^{20}\cdot3^{27}-3\cdot3^{30}\cdot5^{18}}{7\cdot3^{29}\cdot5^{13}-3^{29}\cdot5^{19}}=\dfrac{3^{29}\cdot5^{20}-5^{18}\cdot3^{31}}{3^{29}\cdot5^{13}\cdot7-3^{29}\cdot5^{19}}\)
\(=\dfrac{3^{29}\cdot5^{18}\left(5^2-3^2\right)}{3^{29}\cdot5^{13}\left(7-5^6\right)}=5^5\cdot\dfrac{4^2}{7-5^6}\)
\(P\left(x\right)=A\left(x\right)+B\left(x\right)\)
\(=4x^5+2x^3+x^2-x-x^4-3x^2+2x+5\)
\(=4x^5-x^4+2x^3-2x^2+x+5\)
\(A=3x^2-2x+1\)
\(A=3x^2-2x+\dfrac{1}{3}+\dfrac{2}{3}\)
\(A=3\left(x^2-\dfrac{2x}{3}+\dfrac{1}{9}\right)+\dfrac{2}{3}\)
\(A=3\left(x-\dfrac{1}{3}\right)^2+\dfrac{2}{3}\ge\dfrac{2}{3}\)
Đẳng thức xảy ra khi \(x=\dfrac{1}{3}\)
\(B=x^2-6x+13\)
\(B=x^2-6x+9+4\)
\(B=\left(x-3\right)^2+4\ge4\)
Đẳng thức xảy ra khi \(x=3\)
\(C=2x^2-4x+9\)
\(C=2x^2-4x+2+7\)
\(C=2\left(x^2-2x+1\right)+7\)
\(C=2\left(x-1\right)^2+7\ge7\)
Đẳng thức xảy ra khi \(x=1\)
\(27^6.128^3:12^9\)
\(=\left(3^3\right)^6.\left(2^7\right)^3:\left[3^9.\left(2^2\right)^9\right]\)
\(=3^{18}.2^{21}:\left(3^9.2^{18}\right)\)
\(=\dfrac{3^{18}.2^{21}}{3^9.2^{18}}=3^9.2^3\)
Chúc bạn học tốt!!!