Thực hiện phép tính:
11.3^29-9^15/(2.3^14)^5
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a) 81^11.3^17/27^10.9^15
=(9^2)^11.3^17/(3^3)^10.9^15
=3^44.3^17/3^30.3^30
=3^61/3^60
=3
b) A =( (2^12.3^5 - 2^12.3^4)/ (2^12.3^6 + 2^12.3^5) ) - ((5^10.7^3 - 5^10.7^4)/(5^9.7^3 + 5^9.2^3.7^3))
=(2^12.3^4(3-1))/2^12.3^5(3+1) - 5^10.7^3(1-7)/5^9.7^3(1+8)
=2/12- (-30/9)=1/6 + 10/3 = 7/2
ta co:A = 11.329-915/ (2.314)2
=11.329-(32)15/22.328
=11.329-330/22.328
=329.(11-3)/22.328
= 3.7/4
=21/4
\(\frac{11.3^{22}.3^7-9^{15}}{\left(3^{14}\right)^2}\)
\(=\frac{11.3^{29}-3^{30}}{3^{28}}\)
\(=\frac{3^{29}.\left(11-3\right)}{3^{28}}\)
\(=3.8=24\)
\(\frac{11.3^{22}.3^7-9^{15}}{ \left(3^{14}\right)^2}\)
= \(\frac{11.3.3^{21}.3^7-\left(3^2\right)^{15}}{\left(3^{14}\right)^2}\)
= \(\frac{33.3^{28}-3^{30}}{3^{28}}\)
= \(\frac{33.3^{28}-3^{28}.9}{3^{28}}\)
= \(\frac{3^{28}.\left(33-9\right)}{3^{28}}\)
= \(\frac{24}{1}=24\)
\(\dfrac{11\cdot3^7\cdot9^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
\(=\dfrac{11\cdot3^7\cdot3^{14}-3^{30}}{2^2\cdot3^{28}}\)
\(=\dfrac{3^{21}\left(11-3^9\right)}{2^2\cdot3^{28}}\)
\(=\dfrac{11-3^9}{2^2\cdot3^7}\)
\(A=\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
\(=\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{2^{28}.3^{18}.\left(5-7.2\right)}\)\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.\left(5-14\right)}\)
\(=\frac{2^{29}.3^{18}.\left(5.2-1\right)}{2^{28}.3^{18}.\left(-9\right)}=\frac{2.9}{-9}=-2\)
Vậy A=-2
=\(\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
=\(\frac{2^{29}\left(5.3^{18}-3^{18}\right)}{2^{28}\left(5.3^{18}-3^{18}\right).7}\)
=\(\frac{2}{7}\)