Tính:
A=723.542/1084
B=310.11+310.5/39.24
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2
2 tháng 10 2023
\(a,\dfrac{3^{43}+3^4}{3^{39}+1}\)
\(=\dfrac{3^4\cdot\left(3^{39}+1\right)}{3^{39}+1}\)
\(=3^4\)
\(=81\)
NN
8 tháng 7 2023
\(4^{10}.8^{15}=2^{20}.2^{45}=2^{65}\)
\(4^{15}.5^{30}=2^{30}.5^{30}=10^{30}\)
\(27^{16}:9^{10}=3^{48}:3^{20}=3^{28}\)
\(72^3.54^2=2^9.3^6.2^2.3^6=2^{11}.3^{12}\)
\(108^4=2^8.3^{12}\)
\(3^{10}.11+3^{10}.5=3^{10}.\left(11+5\right)=3^{10}.16\)
\(3^9.2^4=3^9.2^4\)
8 tháng 7 2023
`@` `\text {Ans}`
`\downarrow`
`4^10*8^15`
`= (2^2)^10 * (2^3)^15`
`= 2^20 * 2^45`
`=`\(2^{20+45}=2^{65}\)
`4^15 * 5^30`
`= (2^2)^15 * 5^30`
`= 2^30 * 5^30`
`= (2*5)^30`
`= 10^30`
`27^16 \div 9^10`
`= (3^3)^16 \div (3^2)^10`
`= 3^48 \div 3^20`
`=`\(3^{48-20}=3^{28}\)
`A = `\(72^3\cdot54^2\cdot108^4\)
`= 2^9 * 3^6 * 3^4 * 3^2 * 2^2 * 3^8 * 3^4 * 2^4 * 2^4`
`=`\(\left(2^9\cdot2^2\cdot2^4\cdot2^4\right)\cdot\left(3^6\cdot3^4\cdot3^2\cdot3^8\cdot3^4\right)\)
`= 2^19 * 3^24`
`B = 3^10 * 11 + 3^10 * 5 + 3^9 * 2^4`
`= 3^9 * (11*3 + 5*3 + 2^4)`
`= 3^9 * (33 + 15 + 16)`
`= 3^9 * 64`
`= 27^3 * 4^3`
`= (27 * 4)^3`
`= 108^3`
BV
3
DP
0
\(A=\frac{72^3\times54^2}{108^4}\)
\(\Rightarrow A=\frac{\left(2^3\times3^2\right)^3\times54^2}{\left(54\times2\right)^4}\)
\(\Rightarrow A=\frac{\left(2^3\right)^3\times\left(3^2\right)^3\times54^2}{54^4\times2^4}\)
\(\Rightarrow A=\frac{2^9\times3^6\times54^2}{54^2\times54^2\times2^4}\)
\(\Rightarrow A=\frac{2^5\times3^6}{54^2}\)
\(\Rightarrow A=\frac{2^5\times3^6}{\left(2\times3^3\right)^2}\)
\(\Rightarrow A=\frac{2^2\times2^3\times3^6}{2^2\times\left(3^3\right)^2}\)
\(\Rightarrow A=\frac{2^3\times3^6}{3^6}\)
\(\Rightarrow A=2^3=8\)
\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}\)
\(\Rightarrow B=\frac{3^{10}\times\left(11+5\right)}{3^9\times2^4}\)
\(\Rightarrow B=\frac{3^{10}\times16}{3^9\times16}\)
\(\Rightarrow B=\frac{3^{10}}{3^9}=3\)