a: \(3^7\cdot27^5\cdot81^3=3^7\cdot3^{15}\cdot3^{12}=3^{34}\)
b: \(36^5:18^5=\left(\dfrac{36}{18}\right)^5=2^5=32\)
c: \(24\cdot5^2+5^2\cdot5^3=24\cdot25+25\cdot125=25\cdot149=3725\)
d: \(\dfrac{125^4}{5^8}=\dfrac{5^{12}}{5^8}=5^4=625\)
a) \(3^7.27^5.81^3\)
\(=3^7.\left(3^3\right)^5.\left(3^4\right)^3\)
\(=3^7.3^{15}.3^{12}\)
\(=3^{34}\)
b) \(36^5:18^5\)
\(=\left(\dfrac{36}{18}\right)^5\)
\(=2^5\)
c) \(24.5^5+5^2.5^3\)
\(=24.5^5+5^5\)
\(=5^5.\left(24+1\right)\)
\(=5^5.25\)
\(=5^5.5^2=5^7\)
d) \(125^4:5^8\)
\(=\left(5^3\right)^4:5^8\)
\(=5^{12}:5^8\)
\(=5^4\)
a) 37.275.813=37.315.312=37+15+12=334
b)365:185=(36:18)5=25
c)24.55+52.53
=24.55+55
=55.25
=55.52
=57
=
d)1254:58=512:58=54
a: 37⋅275⋅813=37⋅315⋅312=33437⋅275⋅813=37⋅315⋅312=334
b: 125458=51258=54=625