3. จงหาผลลัพธ์แต่ละข้อต่อไปนี้
1) \(\mathtt{\dfrac{256}{2^5} \times \dfrac{128}{2^8}}\)
วิธีทำ
\(\mathtt{\dfrac{256}{2^5} \times \dfrac{128}{2^8}}\)
= \(\mathtt{\dfrac{2^8}{2^5} \times \dfrac{2^7}{2^8}}\)
= \(\mathtt{\dfrac{2^7}{2^5}}\)
= \(\mathtt{2^{7 \, – \, 5}}\)
= \(\mathtt{2^2}\)
= \(\mathtt{4}\)
ตอบ 4
2) \(\mathtt{(15 \times 3^{-3}) \div (5 \times 3^2)}\)
วิธีทำ
\(\mathtt{(15 \times 3^{-3}) \div (5 \times 3^2)}\)
= \(\mathtt{\dfrac{15 \times 3^{-3}}{5 \times 3^2}}\)
= \(\mathtt{\dfrac{3 \times 3^{-3}}{3^2}}\)
= \(\mathtt{\dfrac{3^{1 \, + \, (-3)}}{3^2}}\)
= \(\mathtt{\dfrac{3^{-2}}{3^2}}\)
= \(\mathtt{3^{-2 \, – \, 2}}\)
= \(\mathtt{3^{-4}}\)
ตอบ \(\mathtt{3^{-4}}\)
3) \(\mathtt{(-1.8 \times 5^2) \div (6 \times 15)}\)
วิธีทำ
\(\mathtt{(-1.8 \times 5^2) \div (6 \times 15)}\)
= \(\mathtt{\dfrac{-1.8 \times 5^2}{6 \times 15}}\)
= \(\mathtt{\dfrac{-0.3 \times 5 \times 5}{15}}\)
= \(\mathtt{\dfrac{-0.3 \times 5}{3}}\)
= \(\mathtt{-0.1 \times 5}\)
= \(\mathtt{-0.5}\)
ตอบ -0.5
4) \(\mathtt{(7^{-2n} \times 7^{5n}) \div (7^{3n} \times 7^n)}\) เมื่อ n เป็นจำนวนเต็มบวก
วิธีทำ
\(\mathtt{(7^{-2n} \times 7^{5n}) \div (7^{3n} \times 7^n)}\)
= \(\mathtt{\dfrac{7^{-2n} \times 7^{5n}}{7^{3n} \times 7^n}}\)
= \(\mathtt{\dfrac{7^{-2n \, + \, 5n}}{7^{3n \, + \, n}}}\)
= \(\mathtt{\dfrac{7^{3n}}{7^{4n}}}\)
= \(\mathtt{7^{3n \, – \, 4n}}\)
= \(\mathtt{7^{-n}}\)
ตอบ \(\mathtt{7^{-n}}\) เมื่อ n เป็นจำนวนเต็มบวก
5) \(\mathtt{\dfrac{8 \, a^5 \, b}{2 \, a^3 \, b^4}}\) เมื่อ \(\mathtt{a \ne 0}\) และ \(\mathtt{b \ne 0}\)
วิธีทำ
\(\mathtt{\dfrac{8 \, a^5 \, b}{2 \, a^3 \, b^4}}\)
= \(\mathtt{4 \, a^{5 \, – \, 3} \, b^{1 \, – \, 4}}\)
= \(\mathtt{4 \, a^2 \, b^{-3}}\)
ตอบ \(\mathtt{4 \, a^2 \, b^{-3}}\) เมื่อ \(\mathtt{a \ne 0}\) และ \(\mathtt{b \ne 0}\)
6) \(\mathtt{\dfrac{26 \, a^6 \, b^7 \, c^2}{2 \, a \, b^3 \, c^3}}\) เมื่อ \(\mathtt{a \ne 0}\), \(\mathtt{b \ne 0}\) และ \(\mathtt{c \ne 0}\)
วิธีทำ
\(\mathtt{\dfrac{26 \, a^6 \, b^7 \, c^2}{2 \, a \, b^3 \, c^3}}\)
= \(\mathtt{13 \, a^{6 \, – \, 1} \, b^{7 \, – \, 3} \, c^{2 \, – 3}}\)
= \(\mathtt{13 \, a^5 \, b^4 \, c^{-1}}\)
ตอบ \(\mathtt{13 \, a^5 \, b^4 \, c^{-1}}\) เมื่อ \(\mathtt{a \ne 0}\), \(\mathtt{b \ne 0}\) และ \(\mathtt{c \ne 0}\)