جواب فعالیت صفحه 107 درس 7 ریاضی هشتم (توان و جذر)

الف

\(\begin{array}{l}{12^4} \div {6^4} = \frac{{{{12}^4}}}{{{6^4}}} = \frac{{12 \times 12 \times 12 \times 12}}{{6 \times 6 \times 6 \times 6}} = \\\\\frac{{12}}{6} \times \frac{{12}}{6} \times \frac{{12}}{6} \times \frac{{12}}{6} = {(\frac{{12}}{6})^4} = {2^4}\end{array}\)

\({3^5} \div {7^5} = \frac{{{3^5}}}{{{7^5}}} = \frac{{3 \times 3 \times 3 \times 3 \times 3}}{{7 \times 7 \times 7 \times 7 \times 7}} = {(\frac{3}{7})^5}\)

\(\begin{array}{l}{( - 4)^3} \div {6^3} = \frac{{{{( - 4)}^3}}}{{{6^3}}} = \frac{{( - 4) \times ( - 4) \times ( - 4)}}{{6 \times 6 \times 6}} = \\\\( - \frac{4}{6}) \times ( - \frac{4}{6}) \times ( - \frac{4}{6}) = {( - \frac{4}{6})^3} = {( - \frac{2}{3})^3}\end{array}\)

\({12^4} \div {6^4} = \frac{{{{12}^4}}}{{{6^4}}} = \frac{{{2^4} \times {6^4}}}{{{6^4}}} = {2^4}\)

ب

\(\begin{array}{l}{8^5} \div {2^5} = {4^5}\\\\{8^5} \div {2^5} = \frac{{{8^5}}}{{{2^5}}} = \frac{{8 \times 8 \times 8 \times 8 \times 8}}{{2 \times 2 \times 2 \times 2 \times 2}} = \\\\\frac{8}{2} \times \frac{8}{2} \times \frac{8}{2} \times \frac{8}{2} \times \frac{8}{2} = {(\frac{8}{2})^5} = {4^5}\end{array}\)

پ

در تقسیم اعداد توان دار با توان های مساوی یکی از توان ها را می نویسیم و پایه ها را بر هم تقسیم می کنیم.

ت

\(\begin{array}{l}{6^8} \div {3^8} = {(\frac{6}{3})^8} = {2^8}\\\\{( - 2)^4} \div \,{( - 3)^4} = {(\frac{{ - 2}}{{ - 3}})^4} = {(\frac{2}{3})^4}\end{array}\)

ث

a و b دو عدد دلخواه و m یک عدد طبیعی و \({a^m} \div {b^m} = {(\frac{a}{b})^{(m)}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b \ne 0\)