1. จงหาผลลัพธ์แต่ละข้อต่อไปนี้ในรูปเลขยกกำลัง
1) \(\mathtt{\dfrac{2^{-5} \, \times \, 2^3 \, \times \, 2^0}{32}}\)
วิธีทำ
\(\mathtt{\dfrac{2^{-5} \, \times \, 2^3 \, \times \, 2^0}{32}}\) = \(\mathtt{\dfrac{2^{-5 \, + \, 3} \, \times \, 1}{2 \, \times \, 2 \, \times \, 2 \, \times \, 2 \, \times \, 2}}\)
= \(\mathtt{\dfrac{2^{-2}}{2^5}}\)
= \(\mathtt{2^{-2 \, – \, 5}}\)
= \(\mathtt{2^{-7}}\)
ตอบ \(\mathtt{2^{-7}}\)
2) \(\mathtt{\dfrac{11^{10} \, \times \, 11^{-1}}{121 \, \times \, 11^5}}\)
วิธีทำ
\(\mathtt{\dfrac{11^{10} \, \times \, 11^{-1}}{121 \, \times \, 11^5}}\) = \(\mathtt{\dfrac{11^{10 \, + \, (-1)}}{(11 \, \times \, 11) \, \times \, 11^5}}\)
= \(\mathtt{\dfrac{11^9}{11^2 \, \times \, 11^5}}\)
= \(\mathtt{\dfrac{11^9}{11^{2 \, + \, 5}}}\)
= \(\mathtt{\dfrac{11^9}{11^7}}\)
= \(\mathtt{11^{9 \, – \, 7}}\)
= \(\mathtt{11^2}\)
ตอบ \(\mathtt{11^2}\)
3) \(\mathtt{\dfrac{(-13)^4 \, \times \, 13^{-2}}{13^3 \, \times \, 13}}\)
วิธีทำ
\(\mathtt{\dfrac{(-13)^4 \, \times \, 13^{-2}}{13^3 \, \times \, 13}}\) = \(\mathtt{\dfrac{13^4 \, \times \, 13^{-2}}{13^{3 \, + \, 1}}}\)
= \(\mathtt{\dfrac{13^{4 \, + \, (-2)}}{13^4}}\)
= \(\mathtt{\dfrac{13^2}{13^4}}\)
= \(\mathtt{13^{2 \, – \, 4}}\)
= \(\mathtt{13^{-2}}\)
ตอบ \(\mathtt{13^{-2}}\)
4) \(\mathtt{\dfrac{(-1,000) \times 10^7 \times (-10)^{-1}}{(-10)^3 \times (-10)^5}}\)
วิธีทำ
\(\mathtt{\dfrac{(-1000) \times 10^7 \times (-10)^{-1}}{(-10)^3 \times (-10)^5}}\)=\(\mathtt{\dfrac{[(-10)\times(-10)\times(-10)] \times 10^7 \times (-10)^{-1}}{(-10)^{3 \, + \, 5}}}\)
= \(\mathtt{\dfrac{(-10)^3 \times 10^7 \times (-10)^{-1}}{(-10)^8}}\)
= \(\mathtt{\dfrac{(-10)^{3 \, + \, (-1)} \times 10^7}{(-10)^8}}\)
= \(\mathtt{\dfrac{(-10)^2 \times 10^7}{(-10)^8}}\)
= \(\mathtt{\dfrac{10^2 \times 10^7}{10^8}}\)
= \(\mathtt{\dfrac{10^{2 \, + \, 7}}{10^8}}\)
= \(\mathtt{\dfrac{10^9}{10^8}}\)
= \(\mathtt{10^{9 \, – \, 8}}\)
= \(\mathtt{10^1}\)
ตอบ \(\mathtt{10^1}\)
5) \(\mathtt{\dfrac{(0.008) \times (0.2)^{-5}}{(-0.2)^2}}\)
วิธีทำ
\(\mathtt{\dfrac{(0.008) \times (0.2)^{-5}}{(-0.2)^2}}\) = \(\mathtt{\dfrac{(0.2 \times 0.2 \times 0.2) \times (0.2)^{-5}}{(0.2)^2}}\)
= \(\mathtt{\dfrac{(0.2)^3 \times (0.2)^{-5}}{(0.2)^2}}\)
= \(\mathtt{\dfrac{(0.2)^{3 \, + \, (-5)}}{(0.2)^2}}\)
= \(\mathtt{\dfrac{(0.2)^{-2}}{(0.2)^2}}\)
= \(\mathtt{(0.2)^{-2 \, – \, 2}}\)
= \(\mathtt{(0.2)^{-4}}\)
ตอบ \(\mathtt{(0.2)^{-4}}\)
6) \(\mathtt{\dfrac{(\frac{1}{2})^3 \times (0.04)^2 \times 5^2}{0.5}}\)
วิธีทำ
\(\mathtt{\dfrac{(\frac{1}{2})^3 \times (0.04)^2 \times 5^2}{0.5}}\) = \(\mathtt{\dfrac{(0.5)^3 \times (0.04)^2 \times 5^2}{0.5}}\)
= \(\mathtt{(0.5)^{3 \, – \, 1} \times (0.04)^2 \times 5^2}\)
= \(\mathtt{(0.5)^2 \times (0.04)^2 \times 5^2}\)
= \(\mathtt{(0.5 \times 0.04 \times 5)^2}\)
= \(\mathtt{(0.1)^2}\)
ตอบ \(\mathtt{(0.1)^2}\)
7) \(\mathtt{\dfrac{a^{-7} \times a^{10}}{a^3 \times a^5}}\) เมื่อ \(\mathtt{a \ne 0}\)
วิธีทำ
\(\mathtt{\dfrac{a^{-7} \times a^{10}}{a^3 \times a^5}}\) = \(\mathtt{\dfrac{a^{-7 \, + \, 10}}{a^{3 \, + \, 5}}}\)
= \(\mathtt{\dfrac{a^3}{a^8}}\)
= \(\mathtt{a^{3 \, – \, 8}}\)
= \(\mathtt{a^{-5}}\)
ตอบ \(\mathtt{a^{-5}}\) เมื่อ \(\mathtt{a \ne 0}\)
8) \(\mathtt{\dfrac{6^{3n} \times 6^{5n}}{6^n \times 6^{2n}}}\) เมื่อ \(\mathtt{n}\) เป็นจำนวนเต็มบวก
วิธีทำ
\(\mathtt{\dfrac{6^{3n} \times 6^{5n}}{6^n \times 6^{2n}}}\) = \(\mathtt{\dfrac{6^{3n \, + \, 5n}}{6^{n \, + \, 2n}}}\)
= \(\mathtt{\dfrac{6^{8n}}{6^{3n}}}\)
= \(\mathtt{6^{8n \, – \, 3n}}\)
= \(\mathtt{6^{5n}}\)
ตอบ \(\mathtt{6^{5n}}\) เมื่อ \(\mathtt{n}\) เป็นจำนวนเต็มบวก