Rút gọn:
a) $\frac{10^2.9-10^2.2}{700}$
b) $\frac{3^9.3^20.2^8}{3^24.243.2^6}$
c) $\frac{2^15.5^3.2^6.3^4}{8.2^18 .81.5}$
Rút gọn:
a) $\frac{10^2.9-10^2.2}{700}$
b) $\frac{3^9.3^20.2^8}{3^24.243.2^6}$
c) $\frac{2^15.5^3.2^6.3^4}{8.2^18 .81.5}$
Đáp án + Giải thích các bước giải:
`a,\frac{10^{2}.9-10^{2}.2}{700}`
`=\frac{10^{2}.(9-2)}{100.7}`
`=\frac{10^{2}.7}{10^{2}.7}`
`=1`
`———-`
`b,\frac{3^{9}.3^{20}.2^{8}}{3^{24}.243.2^{6}}`
`=\frac{3^{9}.3^{20}.2^{8}}{3^{24}.3^{5}.2^{6}}`
`=\frac{3^{29}.2^{8}}{3^{29}.2^{6}}`
`=\frac{3^{29}.2^{6}.2^{2}}{3^{29}.2^{6}}`
`=2^2`
`=4`
`———`
`c,\frac{2^{15}.5^{3}.2^{6}.3^{4}}{8.2^{18}.81.5}`
`=\frac{2^{15}.5^{3}.2^{6}.3^{4}}{2^{3}.2^{18}.3^{4}.5}`
`=\frac{2^{21}.5^{3}.3^{4}}{2^{21}.3^{4}.5}`
`=\frac{2^{21}.3^{4}.5.5^{2}}{2^{21}.3^{4}.5}`
`=5^2`
`=25`
Giải thích các bước giải:
$\begin{array}{l}a)\dfrac{10^2.9-10^2.7}{700}\\=\dfrac{10^2(9-2)}{700}\\=\dfrac{100.7}{100.7}\\=1\\b)\dfrac{3^9.3^{20}.2^8}{3^{24}.243.2^6}\\=\dfrac{3^{29}.2^{8}}{3^{29}.2^6}\\=\dfrac{3^{29}.2^8}{3^{29}.2^{6}}\\=2^2=4\\c)\dfrac{2^{15}.5^3.2^{6}.3^4}{8.2^{18}.81.5}\\=\dfrac{2^{21}.3^4.5^3}{2^3.2^{18}.3^4.5}\\=\dfrac{2^{21}.3^4.5^3}{2^{21}.3^4.5}\\=5^2=25\\\end{array}$