a, 4¹⁰.8¹⁵=2²⁰.2⁴⁵=2⁶⁵

b,4¹⁵.5³⁰=2³⁰.5³⁰=(2.5)³⁰=10³⁰

^{c, \(\frac{2^{10^{ }}.13+2^{10^{ }}.65}{2^{8^{ }}.104}\)}

=\(\frac{2^{10}\left(13+65\right)}{2^8.2^2.26}\) =\(\frac{2^{10}.78}{2^{10}.26}\) =\(\frac{78}{26}\)=3

a) \(\frac{790^4}{79^4}\)

\(=\frac{\left(79.10\right)^4}{79^4}\)

\(=\frac{79^4.10^4}{79^4}\)

\(=10^4\)

\(=10000\)

790^4/79^4

= (79.10)^4/79^4

= 79^4.10^4/79^4

= 10^4

\(A=1+4+4^2+...+4^{90}\)

\(4A=4+4^2+4^3+...+4^{90}+4^{91}\)

\(4A-A=\left(4+4^2+4^3+...+4^{91}\right)-\left(1+4+4^2+...+4^{90}\right)\)

\(3A=4+4^2+4^3+...4^{91}-1-4-4^2-...-4^{90}\)

\(3A=4^{91}-1\)

\(A=\frac{4^{91}-1}{3}\)

t i c k nha ^^

4A= 4+4²+4³+....+4⁹¹

4a-4=(4+4²+4³+...+4⁹¹)-(1+4+4²+...+4⁹⁰)

3a=4⁹¹-1

a=(4⁹¹-1)/3

\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)

\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)

Tử số :     \(4^5.9^4-2.6^9\)

        \(=\left(2^2\right)^5.\left(3^2\right)^4-2.2^9.3^9\)

        \(=2^{10}.3^8-2^{10}.3^9\)

Mẫu số :      \(2^{10}.3^8+6^8.20\)

           \(=2^{10}.3^8+2^8.3^8.2^2.5\)

           \(=2^{10}.3^8+2^{10}.3^8.5\)

             \(=2^{10}.3^8.6\) 

Trl

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