A .
[tex] \frac{ {5}^{2} }{ {5}^{0} } = \\ [/tex]
[tex] \frac{25}{1} = 25 \\ [/tex]
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B .
[tex] {0}^{25} = 0[/tex]
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C .
[tex]( {7 {x}^{0} })^{1} = [/tex]
[tex] ({7 \times 1})^{1} = [/tex]
[tex] {7}^{1} = 7[/tex]
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D .
[tex] ({ {x}^{5} })^{0} = [/tex]
[tex] {x}^{5 \times 0} = [/tex]
[tex] {x}^{0} = 1[/tex]
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Thus the correct option is D.
