Question

calculo para (80 000 000)² (0,0003)

Answer 1

$\ \ \ \ \frac{800000^{2}\times 0,000002}{600000\times0,0002^{4} }\\ \\ = \frac{\big(8\cdot10^5\big)^{2}\times 2\cdot10^{-6}}{6\cdot10^5\times\big(2\cdot10^{-4}\big)^4 } \\ \\=\frac{\big(2^3\cdot10^5\big)^{2}\times 2\cdot10^{-6}}{6\cdot10^5\times\big(2\cdot10^{-4}\big)^{4} } [tex]\ \ \ \ \frac{800000^{2}\times 0,000002}{600000\times0,0002^{4} }\\ \\ = \frac{\big(8\cdot10^5\big)^{2}\times 2\cdot10^{-6}}{6\cdot10^5\times\big(2\cdot10^{-4}\big)^4 } \\ \\=\frac{\big(2^3\cdot10^5\big)^{2}\times 2\cdot10^{-6}}{6\cdot10^5\times\big(2\cdot10^{-4}\big)^{4} }$
$=\frac{2^6\cdot2\times 10^{10}\cdot10^{-6}}{6\cdot2^4\times10^5\cdot10^{-16} } \\ \\=\frac{2^{6+1}\times 10^{10+(-6)}}{6\cdot2^4\times10^{5+(-16)}} } \\ \\=\frac{2^7\times 10^4}{3\cdot2\cdot2^4\times10^{-11} } \\ \\=\frac{2^7\times 10^4}{3\cdot2^{1+4}\times10^{21} } \\ \\=\frac{2^7\times 10^4}{3\cdot2^{5}\times10^{-11} } \\ \\=\frac{2^{7-5}\times 10^{4-(-11)}}{3} \\ \\=\frac{2^{2}\times 10^{15}}{3}\\ \\=\frac{4}{3}\times 10^{15}\\ \\ \approx1,33\times 10^{15}$
----------------------------------------------------------------------------------------$\ \ \ \big(80 000 000\big)^{2} \times\big(0,0003\big)\\ \\=\big(2^{3} \cdot10^{7}\big)^{2} \times3\cdot10^{-4}\\ \\=2^{3\cdot2} \cdot10^{7\cdot2} \times3\cdot10^{-4}\\ \\=2^6 \cdot10^{14} \times3\cdot10^{-4}\\ \\=2^6 \cdot3 \times 10^{14}\cdot10^{-4}\\ \\=64 \cdot3 \times 10^{14+(-4)}\\ \\=192 \times 10^{10}\\ \\=192 \times 10^{10}\cdot \frac{10^{2} }{10^{2}} \\ \\=1,92 \times 10^{10+2} \\ \\=1,92 \times 10^{12}$