a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{3.5.5^4.3^8}=\frac{3^9.5^5}{3^9.5^5}=1\)
c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2\)
\(=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2\)
\(=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=\frac{61}{50}\)
a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=\frac{7^3.5^8}{7^2.5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{5.3.5^4.3^8}=\frac{3^9.5^5}{5^5.3^9}=1\)
c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(-\frac{1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=1,22\)
a. \(\frac{7^3.5^8}{49.25^4}=\frac{7^2.5^8.7}{7^2.\left(5^2\right)^4}=\frac{7^2.5^8.7}{7^2.5^8}=7\)
b. \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^8.25.5^3.3}{5.3.25^2.3^8}=\frac{5^2}{25}=\frac{25}{25}=1\)
c. \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{50}.3^{61}.2+2^{90}.3^{16}.2}=\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2\left(2^{50}.3^{61}+2^{90}.3^{16}\right)}=\frac{1}{2}\)
d. \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(-\frac{1}{10}\right)^2+\frac{11}{10}^2\)
\(=\frac{1}{100}+\frac{121}{100}=\frac{61}{50}\)
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