a) 21^2.14.125/35^5.6
b) 4^9.36+64^4/16^4.100
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1: \(=\dfrac{2^{20}\cdot3^2+2^{24}}{2^{16}\cdot2^2\cdot5^2}=\dfrac{2^{20}\left(3^2+2^4\right)}{2^{18}\cdot5^2}=4\)
2: \(=\dfrac{2^5\left(2^8+1\right)}{2^2\left(2^8+1\right)}=2^3=8\)
3: \(=\dfrac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\dfrac{3^{29}\cdot8}{2^2\cdot3^{28}}=2\cdot3=6\)
A=4^9.36+64^4/16^4.100
A= 262144.36+256.100
A=9437184+25600
A=9462784
\(A=\frac{4^9.36+64^4}{16^4.100}=\frac{2^{20}.\left(9+16\right)}{2^{18}.5^2}=\frac{2^{20}.5^2}{2^{18}.5^2}=2^2=4\)
\(C=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{4^9.36+4^{12}}{4^9.25}=\dfrac{4^9\left(36+4^3\right)}{4^9.25}=\dfrac{100}{25}=4\)
B = 4^9.36+64^4
16^4.100
B = 2^20.(9+16)
2^18.5^2
B = 2^20.5^2
2^18.5^2
B = 2^2
B = 4
D = 4^6.3^4.9^5
6^12
D = 2^12.3^4.9^5
2^12.3^12
D = 2^12.3^14
2^12.3^12
D = 3^2
D = 9
\(\frac{4^9.36+64^4}{16^4.100}=\frac{4^{10}\left(9+8\right)}{4^{10}.25}=\frac{17}{25}\)