Given:
The expression is
[tex](-5)^7\div (-5)^2[/tex]
To find:
The simplified form of the given expression so there is only one positive power for the baser -5.
Solution:
We have,
[tex](-5)^7\div (-5)^2[/tex]
[tex]=\dfrac{(-5)^7}{(-5)^2}[/tex]
Using the properties of exponents, the given expression can be written as
[tex]=(-5)^{7-2}[/tex] [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]
[tex]=(-5)^{5}[/tex]
Here, the base is -5 and the exponent is 5.
Therefore, the correct option is C.
