Answer:
![\displaystyle n^3-\frac{1}{n^{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20n%5E3-%5Cfrac%7B1%7D%7Bn%5E%7B2%7D%7D)
Step-by-step explanation:
<u>Exponents Properties</u>
We need to recall the following properties of exponents:
![(a^x)^y=(a^y)^x=a^{xy}](https://tex.z-dn.net/?f=%28a%5Ex%29%5Ey%3D%28a%5Ey%29%5Ex%3Da%5E%7Bxy%7D)
![\displaystyle a^{-x}=\frac{1}{a^x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%5E%7B-x%7D%3D%5Cfrac%7B1%7D%7Ba%5Ex%7D)
We are given the expression:
![2^m=n](https://tex.z-dn.net/?f=2%5Em%3Dn)
We need to express the following expression in terms of n.
![8^m-4^{-m}](https://tex.z-dn.net/?f=8%5Em-4%5E%7B-m%7D)
It's necessary to modify the expression to use the given equivalence.
Recall
. Thus:
![(2^3)^m-(2^2)^{-m}](https://tex.z-dn.net/?f=%282%5E3%29%5Em-%282%5E2%29%5E%7B-m%7D)
Applying the property:
![(2^m)^3-(2^m)^{-2}](https://tex.z-dn.net/?f=%282%5Em%29%5E3-%282%5Em%29%5E%7B-2%7D)
Substituting the given expression:
![n^3-n^{-2}](https://tex.z-dn.net/?f=n%5E3-n%5E%7B-2%7D)
Or, equivalently:
![\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdisplaystyle%208%5Em-4%5E%7B-m%7D%3D%20n%5E3-%5Cfrac%7B1%7D%7Bn%5E%7B2%7D%7D%7D)
Answer:
Y=1/3
Step-by-step explanation:
X=k/y
So let's make k the subject of formula
k=xy
x=1,y=5
So let's substitute
k=1×5
k=5
So we are to determine the value for y when x is 15
So let's solve
Y=k/x
Y=5/15
Y=1/3
Y=0.333333~0.3
Answer: They are 30% off
Step-by-step explanation:
$124.95 - 30% (37.485)
124.95-37.485= 87.465