Answer:
<em>8 C sometimes</em>
<em>9 64x^8 y^11</em>
<em>10 c 1.28r^2/ t^9</em>
Step-by-step explanation:
<u>Algebraic Operations
</u>
Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:
![\displaystyle \left(\frac{x^n.y^m}{z^p}\right)^q= \frac{x^{qn}.y^{qm}}{z^{qp}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Cfrac%7Bx%5En.y%5Em%7D%7Bz%5Ep%7D%5Cright%29%5Eq%3D%20%5Cfrac%7Bx%5E%7Bqn%7D.y%5E%7Bqm%7D%7D%7Bz%5E%7Bqp%7D%7D)
![\displaystyle \frac{x^n.x^q}{x^p}= x^{n+q-p}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bx%5En.x%5Eq%7D%7Bx%5Ep%7D%3D%20x%5E%7Bn%2Bq-p%7D)
![\displaystyle x^{-n}=\frac{1}{x^n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E%7B-n%7D%3D%5Cfrac%7B1%7D%7Bx%5En%7D)
Let's face the questions at hand
8. A number is raised to a negative exponent is negative?
Following the expressions recalled above, let's pick the expression
![\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%203%5E%7B-2%7D%3D%5Cfrac%7B1%7D%7B3%5E2%7D%3D%5Cfrac%7B1%7D%7B9%7D)
This is a negative power resulting in a positive number
Now we pick
![\displaystyle (-2)^{-3}=\frac{1}{(-2)^3}=-\frac{1}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28-2%29%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B%28-2%29%5E3%7D%3D-%5Cfrac%7B1%7D%7B8%7D)
This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result
<em>Answer: C sometimes
</em>
9 simplify(4xy^2)^3(xy)^5
![(4xy^2)^3(xy)^5=4^3x^3(y^2)^3x^5y^5](https://tex.z-dn.net/?f=%284xy%5E2%29%5E3%28xy%29%5E5%3D4%5E3x%5E3%28y%5E2%29%5E3x%5E5y%5E5)
![=64x^3y^6x^5y^5](https://tex.z-dn.net/?f=%3D64x%5E3y%5E6x%5E5y%5E5)
![=64x^8y^{11}](https://tex.z-dn.net/?f=%3D64x%5E8y%5E%7B11%7D)
10 simplify(2t^-3)^3(0.4r)^2
![(2t^{-3})^3(0.4r)^2=2^3(t^{-3})^30.4^2r^2](https://tex.z-dn.net/?f=%282t%5E%7B-3%7D%29%5E3%280.4r%29%5E2%3D2%5E3%28t%5E%7B-3%7D%29%5E30.4%5E2r%5E2)
![=8t^{-9} 0.16 r^2](https://tex.z-dn.net/?f=%3D8t%5E%7B-9%7D%200.16%20r%5E2)
![=1.28t^{-9} r^2](https://tex.z-dn.net/?f=%3D1.28t%5E%7B-9%7D%20r%5E2)
![\displaystyle \frac{1.28 r^2}{t^9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1.28%20r%5E2%7D%7Bt%5E9%7D)
Answer:
$1200
Step-by-step explanation:
we know that,
I=PTR/100=200*4*3/100=100*4*3=400*3=$1200
5, 3.50+5.50= 9 per person 6 parking so 51-6 for parking = 45 and 45/9= 5
Answer:
x=4
Step-by-step explanation:
Since x+2 is half the size of 3x:
2(x+2)=3x
2x+4=3x
4=3x-2x
x=4
Answer:
I think it's A or B
Step-by-step explanation: