When 27 times x squared times z all over negative 3 times x squared times z to the fourth power is completely simplified, the ex
ponent on the variable z is _____.
Numerical Answers Expected!
I have attached a picture of the problem so it's easier to read.
2 answers:
Answer:
The exponent on the variable z is (-3).
Step-by-step explanation:
Exponent: A quantity representing a power upto which a number of expression is raised often written in superscript of number or an expression..
Given expression:
![\frac{27x^2z}{-3x^2z^4}](https://tex.z-dn.net/?f=%5Cfrac%7B27x%5E2z%7D%7B-3x%5E2z%5E4%7D)
Using identity : ![\frac{a^m}{a^n}=a^{n-m}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bn-m%7D)
![=\frac{27(x)^{2-2}(z)^{1-4}}{-3}=-9x^0z^{-3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B27%28x%29%5E%7B2-2%7D%28z%29%5E%7B1-4%7D%7D%7B-3%7D%3D-9x%5E0z%5E%7B-3%7D)
The exponent on the variable z is (-3).
Isolate z by itself:
![\frac{z}{z^4}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bz%7D%7Bz%5E4%7D%20)
To simplify variables with powers, subtract the smaller power from the bigger power:
![4 - 1 = 3](https://tex.z-dn.net/?f=4%20-%201%20%3D%203)
![\frac{z}{z^4} = \frac{1}{z^3} = z^{-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bz%7D%7Bz%5E4%7D%20%3D%20%5Cfrac%7B1%7D%7Bz%5E3%7D%20%3D%20z%5E%7B-3%7D)
The exponent will be
-3.
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