① احسب:
\[a = 3^2 \times 7 - (1^{13} + 5^0)\]
\[b = (2^3 + 5^{13}) - (2^2 + 5^{13})\]
\[c = 2^2 + 3^2 \times 4 - 2^3\]
\[a = 9 \times 7 - (1 + 1)\]
\[a = 63 - 2\]
\[a = 61\]
\[b = (8 + 5^{13}) - (4 + 5^{13})\]
\[b = (8 - 4)\]
\[b = 4\]
\[c = 4 + 9 \times 4 - 8\]
\[c = 4 + 36 - 8\]
\[c = 32\]
② أكمل الفراغات بالأرقام المناسبة لتكون المساواة صحيحة:
\[100000 \times 10^{\square} = 100^5\]
\[(9^{\square})^3 = 3^{36}\]
\[100000 = 10^5\]
\[100^5 = (10^2)^5 = 10^{10}\]
\[10^5 \times 10^x = 10^{10}\]
\[x = 5\]
\[(9^x)^3 = 3^{36}\]
\[9 = 3^2\]
\[(3^2)^x)^3 = 3^{36}\]
\[3^{6x} = 3^{36}\]
\[6x = 36\]
\[x = 6\]
③ اكتب في صيغة قوة لعدد صحيح طبيعي دليلها مخالف لواحد:
\[d = 3^5 \times 9^{15} \times 27^2\]
\[e = 2^{13} \times 36^5 \times 3^{13}\]
\[f = 5^{2019} \times 3^3 - 5^{2019} \times 2\]
\[d = 3^5 \times (3^2)^{15} \times (3^3)^2\]
\[d = 3^5 \times 3^{30} \times 3^6\]
\[d = 3^{41}\]
\[e = 2^{13} \times (6^2)^5 \times 3^{13}\]
\[e = 2^{13} \times 6^{10} \times 3^{13}\]
\[6^{10} = (2 \times 3)^{10} = 2^{10} \times 3^{10}\]
\[e = 2^{13} \times 2^{10} \times 3^{10} \times 3^{13}\]
\[e = 2^{23} \times 3^{23}\]
\[f = 5^{2019} \times 3^3 - 5^{2019} \times 2\]
\[f = 5^{2019} \times (27 - 2)\]
\[f = 5^{2019} \times 25\]
\[f = 5^{2019} \times 5^2\]
\[f = 5^{2021}\]