[tex]27^4-9^5+3^9[/tex] is divisible by 25
The expression is given as:
[tex]27^4-9^5+3^9[/tex]
Express all terms of the expression as a base of 3
[tex]27^4-9^5+3^9 = (3^3)^4-(3^2)^5+(3^9)[/tex]
Remove the brackets
[tex]27^4-9^5+3^9 = 3^{12}-3^{10}+3^9[/tex]
Factor out 3^9 from the expression
[tex]27^4-9^5+3^9 = 3^9(3^{3}-3^{1}+1)[/tex]
Evaluate all exponents
[tex]27^4-9^5+3^9 = 3^9(27-3+1)[/tex]
Simplify
[tex]27^4-9^5+3^9 = 3^9(25)[/tex]
The above equation means that:
- [tex]27^4-9^5+3^9[/tex] is the product of 3^9 and 25.
- 25 is a factor of [tex]27^4-9^5+3^9[/tex].
Hence, [tex]27^4-9^5+3^9[/tex] is divisible by 25
Read more about factors and multiples at:
https://brainly.com/question/15560501
