Answer:
The laws of exponents are:
a) (x^n)*(x^m) = x^(n + m)
b) (x^n)/(x^m) = x^(n - m)
c) (x^n)^m = x^(n*m)
Now, let's see the given equations:
1) (x-²)-³ = x⁶ (true)
Here we se the third law, the "c"
(x^(-2))^(-3) = x^(-2*-3) = x^6
Then this equation is correct.
2) (a^m)^n = a^m^n (false)
This law does not exist, this is false.
An example of why this is false is:
Let's use the values:
a = 2, m = 1, and n = 2
then, in the left side we have:
(2^1)^2 = (2)^2 = 4
And in the right side we have:
2^(1^2) = 2^(1) = 2
We can see that we have different things in the left side than in the right side, then that relation is false.
3) a⁰ = 0 (false)
Let's rewrite this as:
a^0 = a^(n - n)
Now we can use the second law to rewrite this as:
a^(n - n) = (a^n)/(a^n)
And we have a number divided by the exact same number, we know that this is equal to 1, then:
(a^n)/(a^n) = 1
this means that:
a^0 = 1.
Then this is also false.
The only correct option is the first one.
