[tex] {5}^{12} \times {5}^{8} \\ = {5}^{12 + 8} \\ = {5}^{20} [/tex]
Therefore,
[tex] a) \: {25}^{20} ≠ {5}^{20} [/tex]
[tex]b) ({25}^{5} ) ^{4} \\ = {25}^{5 \times 4} \\ = {25}^{20} \\ ( {25}^{5} )^{4} ≠ {5}^{20} [/tex]
[tex]c) \: ( {5}^{3} . {5}^{2} ) ^{4} \\ = ({5}^{3 + 2}) ^{4} \\ = ({5}^{5} )^{4} \\ = {5}^{20} [/tex]
[tex]d) \: {(5 ^{5}) }^{4} \\ = {5}^{5 \times 4} \\ = {5}^{20} [/tex]
Answers:
[tex]c)( {5}^{3} . {5}^{2} {)}^{4} \\ d) {(5}^{5} ) ^{4} [/tex]
Hope you could understand.
If you have any query, feel free to ask.
