216k views
24 votes
What laws of exponent they are:

1. (x-²)-³ = x⁶
2. (a^m)^n = a^m^n
3. a⁰ = 0


1 Answer

3 votes

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.

User Steven Lyons
by
6.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.