Rút gọn:
8 . 5 - 8 . 2 16
PB
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Rút gọn biểu thức sau: B=8^5×(-5)^8+(-2)^5×10^9/2^16×5^7+20^8
\(B=\dfrac{2^{15}\cdot5^8-2^5\cdot2^9\cdot5^9}{2^{16}\cdot5^7+2^{16}\cdot5^8}=\dfrac{2^{14}\cdot5^8\cdot\left(2-5\right)}{2^{16}\cdot5^7\left(1+5\right)}=\dfrac{1}{4}\cdot5\cdot\dfrac{-1}{2}=\dfrac{-5}{8}\)
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Rút gọn biểu thức sau: A=8^5×(-5)^8+(-2)^5×10^9/2^16×5^7+20^8
rút gọn: 12.(5^2 + 1).(5^4 + 1).(5^8 + 1).(5^16 + 1)
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Rút gọn biểu thức
P= 12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)
\(=\dfrac{5^{32}-1}{2}\)
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\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{32}+1\right)\)
\(2P\)\(=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(2P=\)\(\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(2P=5^{32}-1\)
\(P=\dfrac{5^{32}-1}{2}\)
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Rút gọn rồi so sánh hai phân số sau:
8/16 và 5/2
27(-3/2)^-5 × (-2/5)^-4 ÷ (2/125)
8^5×(-5)^8 + (-2)^5× 10^9/ 2^16× 5^7 +20^8
Rút gọn các biểu thức
Rút gọn lũy thừa:
A = \(\frac{8^5\cdot\left(-5\right)^8+2^5\cdot10}{2^{16}\cdot5^7+20^8}^9\)
\(\frac{2^{15}.5^8+2^{14}.5^9}{2^{16}.5^7+2^{16}.5^8}=\frac{2^{14}.5^8\left(2+5\right)}{2^{16}.5^7\left(1+5\right)}=\frac{2^{14}.5^8.7}{2^{16}.5^7.6}=\frac{5.7}{4.6}=\frac{35}{24}\)
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Rút gọn nhanh Q=12(5^2 + 1)(5^4 + 1)(5^8 + 1)(5^16 + 1)
\(Q=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(\Rightarrow2Q=24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(=5^{32}-1\)
\(Q=\frac{5^{32}-1}{2}\)
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Rút gọn 12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
Rút gọn biểu thức sau:
\(\frac{8^5.\left(-5\right)^8+\left(-2\right)^5.10^9}{2^{16}.5^7+20^8}\)
\(\frac{8^5.\left(-5\right)^8+\left(-2\right)^5.10^9}{2^{16}.5^7+20^8}\)
\(=\frac{\left(2^3\right)^5.5^8+\left(-2\right)^5.\left(2.5\right)^9}{2^{16}.5^7+\left(2^2.5\right)^8}\)
\(=\frac{2^{15}.5^8+\left(-2\right)^5.2^9.5^9}{2^{16}.5^7+2^{16}.5^8}\)
\(=\frac{2^{15}.5^8-2^{14}.5^9}{2^{16}.5^7\left(1+5\right)}\)
\(=\frac{2^{14}.5^8\left(2-5\right)}{2^{16}.5^7.\left(1+5\right)}\)
\(=\frac{2^{14}.5^8.\left(-3\right)}{2^{16}.5^7.6}\)
\(=\frac{-5}{8}\)
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