Math problem?

Question

add

4n^7-9n^6+4
6n^7-6n^6-9
___________

true or false if a is any non zero real number, and n is any integer, then
a^n= _1___
a-n

Answer 1

1)
You have to add the like terms like you do if you have 2a + a = 3a.

You have (4 + 6)n^7 +(-9-6)n^6 +(4-9)

which is 10n^7 - 15n^6 - 5

2) If you mean a^n = 1 / a^(-n) then yes it is true.

Say you have

2*2*2 / 2 that equals 2^3 / 2^1 = 2^2 _= 4
2*2 / 2 that equals 2^2 / 2^1 = 2^1 __ = 2
2 / 2 that equals 2^1 / 2^1 = 2^0 ____=1

Following the pattern:
1 / 2 that equals 2^0 / 2^1 = 2^-1 ___ = 1/2

so 1/2^(1) = 2^(-1)

This is true in general

1/a = 1/a^(-1)

If you put both sides to the -nth power then

(1/a)^(-n) = (1/a^(-1))^(-n)

which simplifies to 1/a^(-n)= a^n (the result we started with)

Answer 2

10^n^7-15n^6-5