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a)\(\frac{36^7}{2^{15}\cdot27^5}=\frac{36^7}{\left(2^3\right)^5\cdot27^5}\)
\(=\frac{36^7}{\left(8\cdot27\right)^5}=\frac{36^7}{216^5}\)
\(=\frac{36^7}{36^5\cdot6^5}=\frac{36^5\cdot36^2}{36^5\cdot6^5}\)
\(=\frac{36^2}{6^5}=\frac{\left(6^2\right)^2}{6^5}=\frac{6^4}{6^5}=\frac{1}{6}\)
\(\)
\(a,\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^8}{2^{15}.3^6}=3^2=9\)
\(b,\frac{6^3+3.6^2+3^3}{-13}=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}=\frac{3^3.2^3+3.3^2.2^2+3^3}{-13}\)
\(=\frac{3^3.2^3+3^3.2^2+3^3}{-13}=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.\left(8+4+1\right)}{-13}=\frac{3^3.13}{-13}=-3^8=\frac{1}{3^8}\)
a.
\(\frac{2^7\times9^3}{6^5\times8^2}=\frac{2^7\times\left(3^2\right)^3}{\left(2\times3\right)^5\times\left(2^3\right)^2}=\frac{2^7\times3^6}{2^5\times3^5\times2^6}=\frac{3}{2^4}=\frac{3}{16}\)
b.
\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{\left(2\times3\right)^3+3\times\left(3\times2\right)^2+3^3}{-13}=\frac{2^3\times3^3+3\times3^2\times2^2+3^3}{-13}=\frac{8\times3^3+3^3\times4+3^3}{-13}\)\(=\frac{3^3\times\left(8+4+1\right)}{-13}=\frac{27\times13}{-13}=-27\)
c.
\(\frac{5^4\times20^4}{25^5\times4^5}=\frac{\left(5\times20\right)^4}{\left(25\times4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
d.
\(\left(\frac{5^4-5^3}{125^4}\right)=\frac{5^3\times\left(5-1\right)}{\left(5^3\right)^4}=\frac{5^3\times4}{5^{12}}=\frac{4}{5^9}\)
a)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}\)
b)\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6.6^2+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^3}{-13}=\frac{6^2.3^2+3.3^2}{-13}=\frac{3^2.\left(6^2+3\right)}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)
c)\(\frac{5^4.20^4}{25^5.4^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
(-10 phần 3 )3.(-6 phần 5)4
=-1000 phần 27.-1296 phần 625
=1296000 phần 16875 bạn tự giuts gọn nhé
2:(1 phần 2 - 2 phần 3)3
=2:(3 phần 6 - 4 phần 6 )3
=2:(-1 phần 6)3
2:-1 phần 216
=2.-216
=-432
63+3.62+33 phần -13
=216+3 . 36+27 phần -13
216+108+27 phần -13
=351 phần -13
=-27
=
2a) \(\frac{3^6+45^4-15^3.4^5}{27^4.25^3+45^6}\)
= \(\frac{3^6+\left(3^2.5\right)^4-\left(3.5\right)^3.\left(2^2\right)^5}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
= \(\frac{3^6+3^8.5^4-3^3.5^3.4^{10}}{3^{12}.5^6-3^{12}.5^6}=\frac{3^3.\left(3^3+3^5.5^4-5^3.4^{10}\right)}{0}\)(xem lại đề)
b) \(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{16}{3}\right)^3:\left(\frac{4}{9}\right)^3}{2^7.5^2+512}\)
= \(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{16}{3}:\frac{4}{9}\right)^3}{2^7.5^2+2^9}\)
= \(\frac{2^7+12^3}{2^7\left(5^2+2^2\right)}\)
= \(\frac{2^7+\left(2^2.3\right)^3}{2^7.29}\)
= \(\frac{2^7+2^6.3^3}{2^7.29}\)
= \(\frac{2^6\left(1+27\right)}{2^7.29}=\frac{28}{2.29}=\frac{14}{29}\)
b) \(\frac{36^7}{2^{15}.27^5}=\frac{\left(2^2.3^2\right)^7}{2^{15}.\left(3^3\right)^5}=\frac{2^{14}.3^{14}}{2^{15}.3^{15}}=\frac{1.1}{2.3}=\frac{1}{6}\)
h) \(\frac{2^{18}.9^4}{6^6.8^4}=\frac{2^{18}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^4}=\frac{2^{18}.3^8}{2^6.3^6.2^{12}}=\frac{2^{18}.3^8}{2^{18}.3^6}=\frac{1.3^2}{1.1}=9\)
o) \(\frac{3^3+3.6^2+6^3}{13}=\frac{3^3+6^2\left(3+6\right)}{13}=\frac{3^3+6^2.3^2}{13}\)
\(=\frac{3^2\left(3+6^2\right)}{13}=\frac{9.3.13}{13}=\frac{9.3.1}{1}=27\)