I know that anything to the power of 0 is 1 but I need help with these 2 questions and check my answers:

(xy)^0 / (z^2a^1)=
(-2mn^2)^1 / (pqm)^0=
(xy^2z)^0= 1?

Negative Exponents: it says to leave answers with positive exponents only, I did all these questions so please check my answers:

y^2*y^-4 = my answer: y^-2 then changed to a positive = 1/y^2

1/m^-2 = m^2/1

x^2y^-1/x^5y^-2= my answer: x^-3y then changed to a positive = y/x^3

(7x^2y^-6)^-1= my answer: -7x^-2 y^6 then changed to a positve= y^6/7x^2

(c^2/3d^-1)^-2 = my answer: c^-4/3d^2 then changed to a positive = 3d^2/c^4

(2m^4n/3m^-1n^3)^-2= my answer:
2m^-8n^-2/3m^2n^-6, I don't know how to change this inot a positve, help

(xy)^0 / (z^2a^1)= 1/(z2a)

-2mn^2)^1 / (pqm)^0= 2mn^2
yes, one.

one the last one, you have to square the 3
others correct.

how do you sqaure the last one?? please show me how

is the last one the only one that is wrong, please show me how to do the last one

Look, the law of exponents applies to all... You had a 3^1 in the denominator, specifically

(3^1...)^-2 and that changes to 9 in the numerator. Law of exponents does not apply to just variables.

so the correct answer would be :

2m^-8n^-2/9m^2n^-6??

I like this last one:

(c^2/3d^-1)^-2 =
c^-4 / (3^-2 d^2)=

9/c^4d^2

check it please.

wait...so you were talking about this question: (c^2/3d^-1)^-2

I thought you were talking about this question:
(2m^4n/3m^-1n^3)^-2

so is my answer to this question (2m^4n/3m^-1n^3)^-2 correct?

how would you turn this question:(2m^4n/3m^-1n^3)^-2 into a positive?

Yess

To solve these exponent problems, it's helpful to remember some basic rules of exponents:

1. Anything raised to the power of 0 is always 1.
2. When dividing with exponents, subtract the exponents.
3. When taking the reciprocal of a term with an exponent, change the sign of the exponent.
4. To remove negative exponents, take the reciprocal of the term and change the sign of the exponent to positive.

Let's go through each of the problems and check your answers:

1. (xy)^0 / (z^2a^1)
Since anything raised to the power of 0 is 1, the numerator becomes 1. The denominator can be simplified as follows:
(z^2a^1) = (z^2)(a^1) = z^2a
Therefore, the expression simplifies to:
1 / (z^2a)

2. (-2mn^2)^1 / (pqm)^0
The numerator can be simplified as follows:
(-2mn^2)^1 = -2mn^2
Since anything raised to the power of 0 is 1, the denominator becomes 1. Therefore, the expression simplifies to:
-2mn^2 / 1 = -2mn^2

3. (xy^2z)^0
Again, since anything raised to the power of 0 is 1, the expression simplifies to:
1

Now, let's check your answers for the negative exponent problems:

1. y^2 * y^-4
To multiply terms with the same base, add the exponents:
y^2 * y^-4 = y^(2 + (-4)) = y^-2
To remove the negative exponent, take the reciprocal:
y^-2 = 1/y^2

2. 1/m^-2
To remove the negative exponent, take the reciprocal and change the sign of the exponent to positive:
1/m^-2 = m^2/1 = m^2

3. x^2y^-1 / x^5y^-2
To divide terms with the same base, subtract the exponents:
x^2y^-1 / x^5y^-2 = x^(2 - 5) * y^(-1 - (-2)) = x^-3 * y
To remove the negative exponent, take the reciprocal:
y/x^3

4. (7x^2y^-6)^-1
To remove the negative exponent, take the reciprocal and change the sign of the exponent to positive:
(7x^2y^-6)^-1 = 1/(7x^2y^-6) = 1/(7x^2 * (1/y^6)) = (1/y^6)/(7x^2) = y^6/7x^2

5. (c^2/3d^-1)^-2
To remove the negative exponent, take the reciprocal and change the sign of the exponent to positive:
(c^2/3d^-1)^-2 = ((c^2)/(3 * (1/d^1)))^-2 = ((c^2 * d^1)/3)^-2 = (3/(c^2 * d^1))^2 = 3^2 / (c^2)^2 * (d^1)^2 = 9 / (c^4 * d^2)

6. (2m^4n/3m^-1n^3)^-2
To simplify this expression, distribute the exponent (2) to each term within the parentheses:
(2m^4n/3m^-1n^3)^-2 = (2^-2 * m^(4*-2) * n^-2) / (3^-2 * m^-1 * n^(3*-2))
Simplifying further:
(2^(-2) * m^(-8) * n^(-2)) / (3^(-2) * m^(-1) * n^(-6))
To remove the negative exponents, take the reciprocal:
(3^2 * m^1 * n^6) / (2^2 * m^8 * n^2)
Simplifying even more:
9m / 4n^4

I hope this clarifies the answers for you. Let me know if you have any further questions!