-225-150:(30+3^2x5)
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a: \(-15-\left(-13+30\right)\)
\(=-15+13-30\)
\(=\left(-15-30\right)+13\)
=-45+13
=-32
b: \(225-150:\left(30+3^2\cdot5\right)\)
\(=225-150:\left(30+9\cdot5\right)\)
\(=225-150:75\)
=225-2
=223
c: \(18\cdot64+18\cdot36-1200\)
\(=18\left(64+36\right)-1200\)
\(=18\cdot100-12\cdot100\)
\(=6\cdot100=600\)
d: \(80-\left[130-\left(12-4\right)^2\right]\)
\(=80-130+\left(12-4\right)^2\)
\(=-50+8^2=64-50=14\)
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\(=\frac{5^3\left(2^3+2+1\right)}{5.11}=\frac{5^3.11}{5.11}=5^2=25\)
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a) \(2^{90}\) và \(5^{30}\)
Ta có : \(2^{90}=2^{\left(3.30\right)}=\left(2^3\right)^{30}=6^{30}\)
Vì \(6^{30}>5^{30}\)
=> \(2^{90}>5^{30}\)
b) \(2^{225}\) và \(3^{150}\)
Ta có : \(2^{225}=2^{\left(3.75\right)}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=3^{\left(2.75\right)}=\left(3^2\right)^{75}=9^{75}\)
Vì \(8^{75}< 9^{75}\)
=> \(2^{225}< 3^{150}\)
c) \(2^{200}\) và \(3^{150}\)
Ta có : \(2^{200}=2^{\left(4.50\right)}=\left(2^4\right)^{50}=16^{50}\)
\(3^{150}=3^{\left(3.50\right)}=\left(3^3\right)^{50}=27^{50}\)
Vì \(16^{50}< 27^{50}\)
=> \(2^{200}< 3^{150}\)
a,\(2^{90}\) và \(5^{30}\)
\(\Leftrightarrow2^{90}=\left(2^3\right)^{30}\);\(5^{30}=\left(5^1\right)^{30}\)
\(\Leftrightarrow\left(2^3\right)^{30}=8^{30};\left(5^1\right)^{30}=5^{30}\)
\(\Rightarrow8^{30}>5^{30}\Rightarrow2^{90}>5^{30}\)
b,\(2^{225}\) và \(3^{150}\)
\(\Leftrightarrow2^{225}=\left(2^3\right)^{75};3^{150}=\left(3^2\right)^{75}\)
\(\Leftrightarrow\left(2^3\right)^{75}=8^{75};\left(3^2\right)^{75}=9^{75}\)
\(\Rightarrow8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)
c,\(2^{200}\) và \(3^{150}\)
\(\Leftrightarrow2^{200}=\left(2^4\right)^{50};3^{150}=\left(3^3\right)^{50}\)
\(\Leftrightarrow\left(2^4\right)^{50}=16^{50};\left(3^3\right)^{50}=27^{50}\)
\(\Rightarrow16^{50}< 27^{50}\Rightarrow2^{200}< 3^{150}\)
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`# \text {Ryo}`
So sánh ạ?
\(2^{225}\text{ và }3^{150}\)
Ta có:
\(2^{225}=2^{3\cdot75}=\left(2^3\right)^{75}=8^{75}\\ 3^{150}=3^{2\cdot75}=\left(3^2\right)^{75}=9^{75}\)
Vì `9 > 8 \Rightarrow`\(9^{75}>8^{75}\)
\(\Rightarrow2^{225}< 3^{150}\)
2²²⁵ = (2³)⁷⁵ = 8⁷⁵
3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵
Do 8 < 9 nên 8⁷⁵ < 9⁷⁵
Vậy 2²²⁵ < 3¹⁵⁰
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\(2^{225}=2^{9.25}=\left(2^9\right)^{25}=512^{25}\)
\(3^{150}=3^{6.25}=\left(3^6\right)^{25}=729^{25}\)
Vì \(512^{25}<729^{25}\)
Vậy \(2^{225}<3^{150}\)
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\(-225-150\div\left(30+3^2\times5\right)\)
\(=\)\(-225-150\div\left(30+9\times5\right)\)
\(=\)\(-225-150\div\left(30+45\right)\)
\(=\)\(-225-150\div75\)
\(=\)\(-225-2\)
\(=\)\(-227\)