a, 20⁵.5¹⁰/100⁵

=20⁵.5⁵.5⁵/100⁵

=100⁵.5⁵/100⁵

=5⁵

=3125

b, (0,9)⁵/(0,3)⁶

=(0,3.3)⁵/0,3⁶

=0,5⁵.3⁵/0,3⁶

=3⁵/0,3

=810

c, 6³+3.6²+3³/-13

=(2.3)³+3.(3.2)²+3³/-13

=2³.3³+3.3².2²+3³/-13

=3³.2³+3³.2²+3³/-13

=3³(2³+2²+1)/-13

=27.13/-13

=-27

d, 4⁶.9⁵+6⁹.120/8⁴.3¹²-6¹¹

=(2²)⁶.(3²)⁵+(2.3)⁹.3.2³.5/(2³)⁴.3¹²-(2.3)¹¹

=2¹².3¹⁰+2⁹.3⁹.3.2³.5/2¹².3¹²-2¹¹.3¹¹

=2¹².3¹⁰+2¹².3¹⁰.5/2¹¹.3¹¹.2.3-2¹¹.3¹¹

=2¹².3¹⁰.(1+5)/2¹¹.3¹¹(6-1)

=2¹².3¹⁰.6/2¹¹.3¹¹.5

=2.6/3.5

=12/15

=4/5

\(A=\frac{25^3.5^5}{6.5^{10}}=\frac{\left(5^2\right)^3.5^5}{6.5^{10}}=\frac{5^6.5^5}{6.5^{10}}=\frac{5^{11}}{6.5^{10}}=\frac{5}{6}\)

\(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.2^3.3^3}{\left(2^3\right)^2.\left(3^2\right)^2}=\frac{2^8.3^3}{2^6.3^4}=\frac{4}{3}\)

\(A=\frac{25^3.5^3}{6.5^{10}}=\frac{5^6.5^3}{6.5^{10}}=\frac{5^9}{6.5.5^9}=\frac{1}{30}\)
\(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.2^3.3^3}{2^6.3^4}=\frac{2^8.3^3}{2^6.3^4}=\frac{2^2}{3}=\frac{4}{3}\)
\(C=\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}=\frac{5^3\left(3^3+3^2-1\right)}{6^3\left(3^3+3^2-1\right)}=\frac{5^3}{6^3}\)

a. \(\frac{20^5.5^{10}}{100^5}\)= \(\frac{20^5.5^{10}}{20^5.5^5}\)= \(5^5\)=\(3125\)

b. \(\frac{0,9^5}{0,3^6}\)= \(\frac{0,9^5}{0,3^5.0,3}\)= \(\left(\frac{0,9}{0,3}\right).\frac{1}{0,3}\)= \(243.\frac{1}{0,3}\)= \(810\)

c.\(\frac{6^3+3.6^2+3^3}{-13}=\frac{\left(3.2\right)^3+3.\left(3.2\right)^{^2}+3^3}{-13}=\frac{3^3.2^3+3.3^2.2^2+3^3}{-13}\)\(=\frac{3^3\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=3^3.\left(-1\right)=-27\)

a) \(\frac{205.5^{10}}{100^5}=\frac{41.5^{11}}{5^2.4}=\frac{41.5^9}{4}\)

b) \(\frac{\left(0,9\right)^5}{\left(0,3\right)^5}=\left(0,9:0,3\right)^5=3^5=243\)

c) \(\frac{6^2+3.6+3^2}{-13}=\frac{2^2.3^2+3.6+3^2}{-13}=\frac{3\left(2^2.3+6+3\right)}{-13}=\frac{3.21}{-13}=\frac{63}{-13}\)

d) \(\frac{4^6.9^5.6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5.\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{24}.3^{20}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{24}.3^{20}.5}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2^{13}.3^9.5}{5}=2^{13}.3^9\)

a. \(\frac{20^5.5^{10}}{100^5}\)

\(=\frac{20^5.\left(5^2\right)^5}{100^5}\)

\(=\frac{20^5.25^5}{100^5}\)

\(=\frac{500^5}{100^5}\)

\(=\left(\frac{500}{100}\right)^5\)

\(=5^5=3125\)

b. \(\frac{\left(0,9\right)^5}{\left(0,3\right)^6}\)

\(=\frac{\left(0,9\right)^5}{\left(0,3\right)^5.0,3}\)

\(=\left(\frac{0,9}{0,3}\right)^5.\frac{1}{0,3}\)

\(=3^5.\frac{1}{0,3}\)

\(=810\)

c. \(\frac{6^3+3.6^2+3^3}{-13}\)

\(=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}\)

\(=\frac{3^3\left(2^3+2^2+1\right)}{-13}\)

\(=\frac{3^3.13}{-13}\)

\(=\left(-3\right)^3\)

\(=-27\)

nhớ cho cả hướng dẫn giải

a: \(A=\dfrac{16^5\cdot15^5}{2^{10}\cdot3^5\cdot5^4}=\dfrac{2^{20}\cdot3^5\cdot5^5}{2^{10}\cdot3^5\cdot5^4}=2^{10}\cdot5=5120\)

b: \(B=\dfrac{2^{15}\cdot3+2^{19}\cdot10}{2^{12}\cdot26}=\dfrac{2^{15}\left(3+2^4\cdot10\right)}{2^{13}\cdot13}=2^2\cdot\dfrac{163}{13}=\dfrac{652}{13}\)

Tính bình thường dc ko bn