Câu 1:

a) 2²²⁵ và 3¹⁵⁰

         Ta có:2²²⁵=(2⁹)²⁵=512²⁵

                  3¹⁵⁰=(3⁶)²⁵=729²⁵

       Vì 512²⁵<729²⁵

                 Suy ra: 2²²⁵<3¹⁵⁰

Câu 2:

a)\(25^3:5^2=\left(5^2\right)^3:5^2=5^6:5^2=5^4\)

b)\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)

c)\(3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3+\frac{1}{4}:2=3+\frac{1}{8}=\frac{25}{8}\)

Câu 3:

a)\(9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^2.\left(\frac{1}{3^4}\right)=3^7:3^4=3^3\)

b)\(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.\frac{1}{2^4}\right)=2^7:\frac{1}{2}=2^8\)

c)\(3^2.2^5.\left(\frac{2}{3}\right)^2=288.\frac{4}{9}=2^7\)

d)\(\left(\frac{1}{3}\right)^3.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^4.\left(3^2\right)^2=3^4.\left(\frac{1}{3}\right)^4=3^4:3^4=1\)

a. 2\(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}:2^0\right):2^3\)

= \(\left(\frac12+\frac13\right):\left(\frac12-\frac13\right)+\left(\frac12:1\right):8\)

=\(\left(\frac36+\frac26\right):\left(\frac36-\frac26\right)+\left(\frac12\right):8\)

= \(\left(\frac56:\frac16\right)+\left(\frac{1}{2_{}}\right):8\)

= \(5+\frac12:8\)

= \(5+\frac{1}{16}\)

= \(\frac51+\frac{1}{16}=\frac{80}{16}+\frac{1}{16}=\frac{81}{16}\)

a) 2187

b)243/3125

c)4871/891

d)75

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