Negative Exponents Math HELP!!!!?

Question

What do this equal: 5z‾³
AND what do this equal: (5z)‾³
They DONT equal the same thing!!

If you give me the correct answer!! 10 POINTS!!!!

Just BASIC 7th grade math!!!

Answer 1

The first one, 5 times z to the power of negative three, is equal to 1 divided by 5 times z to the power of a positive three.

The second is one over 5z to the power of positive three.

Answer 2

No they dont equal the same thing

5z‾³ = 5/z^^3

(5z)‾³ = 1 / ( 5z) ^^ 3 = 1 / 125z^^3

Answer 3

The answer is very tricky. In 5z‾³, it is basically telling you 5 times z‾³, which is (5)/(z³). With (5z)‾³, it is telling you that it is (5z) to the power of negative three. The answer is (1)/[(5z)³] or 1/(125z³). Hope that helps

Answer 4

David is correct. To understand why negative powers work like this, consider that dividing a power term by its base reduces the exponent by one. So for example (assuming a non-zero z):

z^3 / z = z^(3-1) = z^2
z^2 / z = z^(2-1) = z^1 (=z)
z^1 / z = z^(1-1) = z^0 (=1)
z^0 / z = z^(0-1) = z^-1 (= 1/z)
z^-1 / z = z^(-1-1) = z^-2 (= 1/z^2)

Etc.

Answer 5

5z^-3 = 5(1/z^3) = 5/z^3

(5z)^-3 = 1/(5z^3)

Answer 6

Well, it has to do with order of operations

The first one is like this. Five times Z to the negative third power

The second one is like this. The product of Five times Z, all taken to the negative third power.

That seriously changes the equation.

Answer 7

Remember the rules:
1) a^(-n)=1/(a^n)
Ex. 5^-2=1/(5^2)=1/25.
2) (ab)^n = a^n * b^n
Ex. (7a)^2 = 7^2 * a^2 = 49a^2.

And remember the order of operations.

Answer 8

(5x)^3 =5^3*x^3 = 125x^3

5x^3 = 5x^3.