Option C:
[tex]-5^{5}[/tex]
Solution:
Given expression is [tex]-5^7\div-5^2[/tex].
To simplify the given expression.
Using exponent rule: [tex]a^m\div a^n = a^{m-n}[/tex]
[tex]-5^7\div-5^2[/tex]
Here the bases are same (–5), so we can subtract the powers of the bases.
[tex]-5^7\div-5^2=-5^{7-2}[/tex]
[tex]=-5^{5}[/tex]
The positive power of the base –5 is 5.
Option C is the correct answer.
Hence the simplified form of [tex]-5^7\div-5^2[/tex] is [tex]-5^5[/tex].
