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a: \(A=\dfrac{16^5\cdot15^5}{2^{10}\cdot3^5\cdot5^4}=\dfrac{2^{20}\cdot3^5\cdot5^5}{2^{10}\cdot3^5\cdot5^4}=2^{10}\cdot5=5120\)
b: \(B=\dfrac{2^{15}\cdot3+2^{19}\cdot10}{2^{12}\cdot26}=\dfrac{2^{15}\left(3+2^4\cdot10\right)}{2^{13}\cdot13}=2^2\cdot\dfrac{163}{13}=\dfrac{652}{13}\)
1) \(=\frac{6^5.5^3\left(1+5\right)}{6^5.5^3.3}=\frac{6}{3}=2\)
2)
\(2B=2+2^2+2^3+...+2^{101}\)
\(2B-B=B=\left(2+2^2+...+2^{101}\right)-\left(1+2+...+2^{100}\right)=2^{101}-1\)
(0.6)^5/(0.2)^6
= [(0.2)^5. 3^5]/(0.2)^6
= 3^5/0.2
=243/0.2
= 1215
6^3+3.6^2+3^3/-13
= 2^3.3^3+3.2^2.3^2+3^3/-13
=3^3(2^3+2^2+1)/-13
=3^3.13/-13
=-27
\(\frac{6^3+3\cdot6^2+3^3}{-13}=\frac{\left(3\cdot2\right)^3+3\cdot\left(3\cdot2\right)^2+3^3}{-13}=\frac{3^3\cdot2^3+3\cdot3^2\cdot2^2+3^3}{-13}=\frac{3^3\cdot\left(2^3+2^2+1\right)}{-13}=\frac{27\cdot13}{-13}=-27\)