Tính: 7mũ 3 .9+3 mũ 2.7 mũ 4-45.539
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\((3.x-2^{4} ):7^3 =2.7^{4}\)
\(=>(3.x-16):7^{3} =2.7^{4}\)
\(=>3.x-16=2.7^{4}:7^{3}\)
\(=>3.x-16=2.7^{4-3}\)
\(=>3.x-16=2.7\)
\(=>3.x-16=14\)
\(=>3.x=14+16\)
\(=>3.x=30\)
\(=>x=30:3\)
\(=>x=10\)
\(\left(3x-2^4\right):7^3=\left(2.7\right)^4\)
\(\Rightarrow\left(3x-2^4\right)=2^4.7^4.7^3\)
\(\Rightarrow3x-2^4=2^4.7^7\)
\(\Rightarrow3x=2^4.7^7+2^4\)
\(\Rightarrow3x=2^4.\left(7^7+1\right)=16\left(7^7+1\right)\)
\(\Rightarrow x=\dfrac{16\left(7^7+1\right)}{3}\)
\(\left(3x-2^4\right).7^3=2.7^4\)
\(\Rightarrow\left(3x-2^4\right)=2.7^4:7^3=14\)
\(\Rightarrow\)\(3x=14+16=30\)
\(\Rightarrow x=30:3=10\)
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a) \(7^5.7^6=7^{5+6}=7^{11}\)
b) \(5^{20}.5=5^{20+1}=5^{21}\)
c) \(7^9:7=7^{9-1}=7^8\)
d) \(25^3.5^2=\left(5^2\right)^3.5^2=5^{2.3}.5^2=5^6.5^2=5^{6+2}=5^8\)
a) \(\left(7^{60}:7^{14}\right):7^{12}\)
\(=7^{46}:7^{12}=7^{34}\)
b) \(\left(5^{32}.5^9\right):\left(5^{48}.25\right)\)
\(=\left(5^{32}.5^9\right):\left(5^{48}.5^2\right)\)
\(=5^{41}:5^{50}=-\left(5^9\right)\)
c) \(\left(11^{154}-11^{152}\right):11^{152}\)
= \(\left(11^{152}.121-11^{152}\right):11^{152}\)
=\(\left[11^{152}.\left(121-1\right)\right]:11^{152}\)
= \(11^{152}.120:11^{152}\)
= \(120\)
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