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[tex] {3}^{21} \times {5}^{21} - {15}^{21} = {(3 \times 5)}^{21} - {15}^{21} = {15}^{21} - {15}^{21} = 0[/tex]

[tex] {3}^{20} \times {2}^{20} - {6}^{23} \div {6}^{3} = {(3 \times 2)}^{20} - {6}^{23} \div {6}^{3} = {6}^{20} - {6}^{20} = 0[/tex]

[tex] {2}^{18} \times {12}^{18} \div ( {6}^{16} \times {4}^{16} ) = {24}^{18} \div {24}^{16} = {24}^{2} = 576[/tex]

[tex] {75}^{38} \div {25}^{38} - { ({3}^{19}) }^{2} = {3}^{38} - {3}^{38} = 0[/tex]

[tex] {26}^{27} \div {13}^{27} \div {2}^{ {5}^{2} } = {2}^{27} \div {2}^{25} = {2}^{2} = 4[/tex]

[tex] {10}^{64} \div {2}^{64} - {5}^{ {4}^{3} } = {5}^{64} - {5}^{64} = 0[/tex]

b) 3^20×2^20-6^23:6^3=

=(3×2)^20-6^23+3=

=6^20-6^20=

=0

c) 2^18×12^18:(6^16×4^16)=

=(2×12)^18:[(6×4)^16]=

=24^18:24^16=

=24^18-16=

=24^2=

=576

d) 75^38:25^38-(3^19)^2=

=(75:25)^38-3^19×2=

=3^38-3^38=

=0

e) 26^27:13^27:2^5^2=

=(26:13)^27:2^25=

=2^27:2^25=

=2^27-25=

=2^2=

=4

f)10^64:2^64-5^4^3=

=(10:2)^64-5^64=

=5^64-5^64=

=0

Explicație pas cu pas:

REGULI DE CALCUL CU PUTERI:

a^m×a^n=a^m+n

a^m:a^n=a^m-n

(a^m)^n=a^m×n

a^n×b^n=(a×b)^n

a^n:b^n=(a:b)^n