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\(\frac{A}{B}=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(\frac{A}{B}=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}\)
\(\frac{A}{B}=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(\frac{A}{B}=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
\(\frac{A}{B}=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)
\(\frac{A}{B}=\frac{2^{29}.3^{18}.\left(10-9\right)}{2^{28}.3^{18}.\left(15-14\right)}=2\)
\(a,2^{x+2}-2^x=96\)
\(=>2^x.2^2-2^x=96\)
\(=>2^x.\left(4-1\right)=96\)
\(=>2^x.3=96\)
\(=>2^x=96:3=32\)
\(=>2^x=2^5\)
\(=>x=5\)
\(b,720:\left[41.\left(2x-5\right)\right]=2^3.125:5^2\)
\(=>720:\left[41.\left(2x-5\right)\right]=8.125:25\)
\(=>720:\left[41.\left(2x-5\right)\right]=8.5=40\)
\(=>41.\left(2x-5\right)=720:40=18\)
\(=>2x-5=18:41=\frac{18}{41}\)
\(=>2x=\frac{18}{41}+5=\frac{223}{41}\)
\(=>x=\frac{223}{41}:2=\frac{223}{62}\)
\(c,\left(-2x+7\right)^{19}=\left(-2x+7\right)^{19}.\left(x+1\frac{1}{4}\right)^2\)
\(=>\left(-2x+7\right)^{19}:\left(-2x+7\right)^{19}=\left(x+\frac{5}{4}\right)^2\)
\(=>1=\left(x+\frac{5}{4}\right)^2\)
\(=>1^2=\left(x+\frac{5}{4}\right)^2\)
\(=>1=x+\frac{5}{4}\)
\(=>x=1-\frac{5}{4}=-\frac{1}{4}\)
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Và giữ đúng lời hứa trên@@!!!!!