Tính :
A = \(\frac{25^3.5^5}{6.5^{10}}\)
dễ quá nha
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= \(\frac{5^6.5^5}{6.5^{10}}\) = \(\frac{5^{11}}{6.5^{10}}\)= \(\frac{5}{6}\)
\(A=\frac{25^3.5^5}{6.5^{10}}=\frac{\left(5^2\right)^3.5^5}{6.5^{10}}=\frac{5^6.5^5}{6.5^{10}}=\frac{5^{11}}{6.5^{10}}=\frac{5}{6}\)
\(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.2^3.3^3}{\left(2^3\right)^2.\left(3^2\right)^2}=\frac{2^8.3^3}{2^6.3^4}=\frac{4}{3}\)
#)Giải :
a)\(2^6.5^6=\left(2.5\right)^6=10^6\)
b)\(8^2.5^2=\left(8.5\right)^2=40^2\)
c)\(4^3.5^3=\left(4.5\right)^3=20^3\)
d)\(5^2.6^2.3^2=\left(5.6.2\right)^2=60^2\)
e)\(\frac{625^5}{25^8}=\frac{\left(25^2\right)^5}{25^8}=\frac{25^{10}}{25^8}=25^2\)
g)\(\frac{3^9}{7}.\frac{7^9}{3}=\frac{\left(3.7\right)^9}{7.3}=\frac{21^9}{21}=21^8\)
\(\frac{2^2.3^3.5^7}{2^3.3^4.5^6}=\frac{1.1.5}{2.3.1}=\frac{5}{6}\)
Làm tương tự
\(6.5+1.2+3.5-5.2+6.5-4.8\)
\(=30+2+15-10+30-32\)
\(=\left(30+2\right)+\left(15-10+30\right)-32\)
\(=32+35-32\)
\(=\left(32-32\right)+35\)
\(=0+35\)
\(=35\)
a . Ta có : \(A=\frac{25^3.5^5}{6.5^{10}}=\frac{5^{11}}{6.5^{10}}=\frac{5}{6}\)
b . Ta có : \(B=\frac{2^6.6^3}{8^2.9^2}=\frac{2^5.\left(2.3\right)^3}{\left(2^3\right)^2.\left(3^2\right)^2}=\frac{2^8.3^3}{2^6.3^4}=\frac{4}{3}\)
c . Ta có :
\(C=\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}=\frac{\left(3.5\right)^3+5.\left(3.5\right)^2-5^3}{\left(6.3\right)^3+6.\left(3.6\right)^2-6^3}=\frac{5^3.\left(3^3-3^2-1\right)}{6^3.\left(3^3+3^2-1\right)}=\frac{5^3}{6^3}\)
d . Ta có :
\(D=\frac{\left(7^4-7^3\right)^2}{49^3}=\frac{7^4-7^3}{49^3}.\left(7^4-7^3\right)=\left(\frac{7^4}{49^3}-\frac{7^3}{49^3}\right).\left(7^4-7^3\right)\)
\(=\left(\frac{7^4}{7^6}-\frac{7^3}{7^6}\right).\left(7^4-7^3\right)=\left(\frac{1}{7^2}-\frac{1}{7^3}\right).\left(7^4-7^3\right)\)
\(=\frac{6}{7^3}.\left(7^4-7^3\right)=\frac{6}{7^3}.7^3.\left(7-1\right)=36\)
a) \(A=\frac{\left(5^2\right)^3.5^5}{6.5^{10}}=\frac{5^6.5^5}{6.5^{10}}=\frac{5^{11}}{6.5^{10}}=\frac{5}{6}\)
b) \(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.\left(2.3\right)^3}{\left(2^3\right)^2.\left(3^2\right)^2}=\frac{2^5.2^3.3^3}{2^6.3^4}=\frac{2^8.3^3}{2^6.3^4}=\frac{2^2}{3}=\frac{4}{3}\)
\(A=\frac{\left(5^2\right)^3\cdot5^5}{6\cdot5^{10}}\)
\(A=\frac{5^{2+3}\cdot5^5}{6\cdot5^{10}}\)
\(A=\frac{5^5\cdot5^5}{6\cdot5^{10}}\)
\(A=\frac{5^{5+5}}{6\cdot5^{10}}\)
\(A=\frac{5^{10}}{6\cdot5^{10}}\)
\(\Rightarrow A=\frac{1}{6}\)
\(A=\frac{25^3.5^5}{6.5^{10}}=\frac{\left(5^2\right)^3.5^5}{6.5^{10}}=\frac{5^5.5^5}{6.5^{10}}=\frac{1}{6}.\)