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\(\frac{15^5.10^5}{6^6.25^6}\)
\(=\frac{3^5.5^5.2^5.5^5}{3^6.2^6.5^{12}}\)
\(=\frac{3^5.2^5.5^{10}}{3^6.2^6.5^{12}}\)
\(=\frac{1}{3.2.5^2}\)
\(\frac{\left(5^4.5^3\right)^3}{125^4}\)
\(=\frac{\left(5^7\right)^3}{5^{12}}\)
\(=\frac{5^{21}}{5^{12}}\)
\(=5^9\)
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https://khoahoc.vietjack.com/question/661489/bieu-thuc-a-3-45-9-6-7-4-3-12-5-11-3-co-gia-tri-3-11
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a) \(\dfrac{27^3\cdot11+9^5\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot\left(11+3\cdot5\right)}{3^9\cdot2^4}\)
\(=\dfrac{11+15}{16}\)
\(=\dfrac{26}{16}\)
\(=\dfrac{13}{8}\)
b) \(\dfrac{5^8+2^2\cdot25^4+2^3\cdot125^3-15^4\cdot5^4}{4^2\cdot625^2}\)
\(=\dfrac{5^8+2^2\cdot5^8+2^3\cdot5^9-3^4\cdot5^4\cdot5^4}{2^4\cdot5^8}\)
\(=\dfrac{5^8\cdot\left(1+2^2+2^3\cdot5-3^4\right)}{5^8\cdot2^4}\)
\(=\dfrac{1+4+40-81}{16}\)
\(=\dfrac{-36}{16}\)
\(=\dfrac{-9}{4}\)
c) \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\cdot\left(1-3\right)}{2^{10}\cdot3^8\cdot\left(1+5\right)}\)
\(=\dfrac{-2}{6}\)
\(=-\dfrac{1}{3}\)
\(\frac{3^4.5-3^6}{3^4.13+3^4}=\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}=\frac{5-9}{14}=-\frac{4}{14}=-\frac{2}{7}\)