( 5^ 3 + 5 ^ 4 + 125 ^2 ) : 5 ^ 3 = ?
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PP
0
T
10 tháng 9 2023
\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)
\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)
\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)
\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)
\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)
\(=0,2-\dfrac{2}{3}\)
\(=-\dfrac{7}{15}\)
\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)
\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)
\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)
\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)
\(=\dfrac{13}{26}\)
\(=\dfrac{1}{2}\)
#\(Toru\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
10 tháng 9 2023
\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)
15 tháng 10 2023
a: \(3^7\cdot27^5\cdot81^3=3^7\cdot3^{15}\cdot3^{12}=3^{34}\)
b: \(36^5:18^5=\left(\dfrac{36}{18}\right)^5=2^5=32\)
c: \(24\cdot5^2+5^2\cdot5^3=24\cdot25+25\cdot125=25\cdot149=3725\)
d: \(\dfrac{125^4}{5^8}=\dfrac{5^{12}}{5^8}=5^4=625\)
VN
Võ Ngọc Phương
CTVHS
VIP
15 tháng 10 2023
a) \(3^7.27^5.81^3\)
\(=3^7.\left(3^3\right)^5.\left(3^4\right)^3\)
\(=3^7.3^{15}.3^{12}\)
\(=3^{34}\)
b) \(36^5:18^5\)
\(=\left(\dfrac{36}{18}\right)^5\)
\(=2^5\)
c) \(24.5^5+5^2.5^3\)
\(=24.5^5+5^5\)
\(=5^5.\left(24+1\right)\)
\(=5^5.25\)
\(=5^5.5^2=5^7\)
d) \(125^4:5^8\)
\(=\left(5^3\right)^4:5^8\)
\(=5^{12}:5^8\)
\(=5^4\)
TL
B={[5^10. 7^3 - 25^2 . 49^2] : [(125 . 7)^3+5^9 . 14^3]} - {[2^12-4^6 . 9^2] : [(2^2.3)^6+8^4 . 3^5]
1
9 tháng 7 2023
Sửa đề: \(5^9\cdot49^2\)
\(=\dfrac{5^{10}\cdot7^3-5^9\cdot7^4}{5^9\cdot7^3+5^9\cdot14^3}-\dfrac{2^{12}-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}\)
\(=\dfrac{5^9\cdot7^3\left(5-7\right)}{5^9\cdot7^3\left(1+8\right)}-\dfrac{2^{12}\left(1-3^4\right)}{2^{12}\left(3^6+3^5\right)}=\dfrac{-2}{9}+\dfrac{80}{972}\)
=-34/243
\(\left(5^3+5^4+125^2\right):5^3\)
\(=\left[5^3+5^4+\left(5^3\right)^2\right]:5^3\)
\(=\left(5^3+5^4+5^6\right):5^3\)
\(=5^3\times\left(1+5+5^3\right):5^3\)
\(=1+5+5^3\)
\(=131\)
\(\left(5^3+5^4+125^2\right):5^3=\left(5^3+5^4+5^6\right):5^3\)
\(=5^3\left(1+5+5^3\right):5^3=1+5+125\)
\(=131\)