جواب تمرین صفحه 67 درس 4 ریاضی نهم (توان و ریشه)

الف

 \(\begin{array}{l}\frac{{{3^{ - 5}} \times {{10}^{ - 5}} \times 25}}{{{4^{ - 5}} \times {{15}^{ - 5}}}} = \frac{{{{30}^{ - 5}} \times {5^2}}}{{{{60}^{ - 5}}}} = \\\\{\left( {\frac{{30}}{{60}}} \right)^{ - 5}} \times {5^2} = {\left( {\frac{1}{2}} \right)^{ - 5}} \times 25 = \\\\{2^5} \times 25 = 32 \times 25 = 800\end{array}\) 

ب

\(\begin{array}{l}\frac{{{8^{ - 1}} \times {4^2}}}{{{2^{ - 4}} \times \frac{1}{8}}} = \frac{{{2^4} \times {{({2^2})}^2}}}{{{8^1} \times {8^{ - 1}}}} = \\\\\frac{{{2^4} \times {2^4}}}{{{8^0}}} = \frac{{{2^8}}}{1} = 256\end{array}\)

عبارات صحیح از قرار زیر هستند:

\(\begin{array}{l}4/3 \times {10^3} = 4300\\\\6/18 \times {10^7} = 61800000\\\\5/9 \times {10^{ - 1}} = 0/59\\\\8/2570 \times {10^4} = 82570\;\end{array}\)

\(6/95 \times {10^{5}}\) کیلومتر

\(5 \times {10^{ - 7}}\) متر

قطر خورشید 107 برابر زمین است.

\(\begin{array}{l}2 \times {10^{ - 7}} \times 4 \times {10^9} = 8 \times \left( {{{10}^{ - 7}} \times {{10}^9}} \right) = 8 \times {10^2}\\\\\frac{{12/5 \times {{10}^{ - 4}}}}{{25 \times {{10}^{ - 19}}}} = \frac{{125 \times {{10}^{ - 5}}}}{{25 \times {{10}^{ - 19}}}} = 5 \times \frac{{{{10}^{19}}}}{{{{10}^5}}} = 5 \times {10^{14}}\end{array}\)

\(6/287 \times {10^8} = 62/87 \times {10^7} > 9/17 \times {10^7}\)

نتیجه می گیریم، مریخ به زمین نزدیک تر است.

\(\begin{array}{l}0/02 < 2/7 \times {10^{ - 2}} < 2/7 \times {10^{ - 1}} < 2/7 \times {10^0} < 2/7 \times {10^1} < 2/7 \times {10^2} < \ldots \\\\ \Rightarrow \,\,\,\bigcirc = - 2\,,\, - 1\,,\,0\,,\,1\,,\,2\,,\,...\end{array}\)

\(\begin{array}{l}0/03 = 0/003 \times {10^1} > 0/003 \times {10^{ - 1}} > 0/003 \times {10^{ - 2}} > 0/003 \times {10^{ - 3}} > \ldots \\\\ \Rightarrow \,\,\,\bigcirc = - 1\,,\, - 2\,,\, - 3\,,\, - 4\,,\,...\end{array}\)

\(\begin{array}{l}1/5 \times {10^{ - 2}} = 15 \times {10^{ - 3}}\\\\1/2 \times {10^6} = 1200000 = 1200000000 \times {10^{ - 3}}\\\\5/35 \times {10^{ - 3}}\\\\3/7 \times {10^{ - 2}} = 37 \times {10^{ - 3}}\\\\ \Rightarrow \;5/35 \times {10^{ - 3}} < 15 \times {10^{ - 3}} < 37 \times {10^{ - 3}} < 1200000\\\\ \Rightarrow 5/35 \times {10^{ - 3}} < 1/5 \times {10^{ - 5}} < 3/7 \times {10^{ - 2}} < \;1/2 \times {10^6}\end{array}\)