So here are a few rules with exponents that you should know:
- Multiplying exponents of the same base:
![x^m*x^n=x^{m+n}](https://tex.z-dn.net/?f=%20x%5Em%2Ax%5En%3Dx%5E%7Bm%2Bn%7D%20)
- Dividing exponents of the same base:
![x^m\div x^n=x^{m-n}](https://tex.z-dn.net/?f=%20x%5Em%5Cdiv%20x%5En%3Dx%5E%7Bm-n%7D%20)
- Powering a power to a power:
![(x^m)^n=x^{m*n}](https://tex.z-dn.net/?f=%20%28x%5Em%29%5En%3Dx%5E%7Bm%2An%7D%20)
- Converting a negative exponent to a positive one:
![x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m](https://tex.z-dn.net/?f=%20x%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Bx%5Em%7D%5C%20%5Ctextsf%7Band%7D%5C%20%5Cfrac%7B1%7D%7Bx%5E%7B-m%7D%7D%3Dx%5Em%20)
<h2>1.</h2>
Firstly, solve the outside exponent:
![(2x^3y^7)^{-2}=2^{-2}x^{3*-2}y^{7*-2}=2^{-2}x^{-6}y^{-14}](https://tex.z-dn.net/?f=%20%282x%5E3y%5E7%29%5E%7B-2%7D%3D2%5E%7B-2%7Dx%5E%7B3%2A-2%7Dy%5E%7B7%2A-2%7D%3D2%5E%7B-2%7Dx%5E%7B-6%7Dy%5E%7B-14%7D%20)
Next, convert the negative exponents into positive ones:
![2^{-2}x^{-6}y^{-14}=\frac{1}{2^2x^6y^{14}}=\frac{1}{4x^6y^{14}}](https://tex.z-dn.net/?f=%202%5E%7B-2%7Dx%5E%7B-6%7Dy%5E%7B-14%7D%3D%5Cfrac%7B1%7D%7B2%5E2x%5E6y%5E%7B14%7D%7D%3D%5Cfrac%7B1%7D%7B4x%5E6y%5E%7B14%7D%7D%20)
<u>Your final answer is
</u>
<h2>2.</h2>
For this, just divide:
![\frac{12x^5y^3}{4x^{-1}}=\frac{12}{4}x^{5-(-1)}y^{3-0}=3x^6y^3](https://tex.z-dn.net/?f=%20%5Cfrac%7B12x%5E5y%5E3%7D%7B4x%5E%7B-1%7D%7D%3D%5Cfrac%7B12%7D%7B4%7Dx%5E%7B5-%28-1%29%7Dy%5E%7B3-0%7D%3D3x%5E6y%5E3%20)
<u>Your final answer is
</u>
<h2>3.</h2>
For this, convert all negative exponents into positive ones:
![\frac{r^{-7}b^{-8}}{t^{-4}w}=\frac{t^4}{r^7b^8w}](https://tex.z-dn.net/?f=%20%5Cfrac%7Br%5E%7B-7%7Db%5E%7B-8%7D%7D%7Bt%5E%7B-4%7Dw%7D%3D%5Cfrac%7Bt%5E4%7D%7Br%5E7b%5E8w%7D%20)
<u>Your final answer is
</u>
Answer:
Step-by-step explanation:
The line BD divides a right angle into two acute angles <CBD + <DBA
They add to 90.
They are therefore complementary.
The word you are looking for is complementary.
The sum of the rational expression is
X=4
Answer:
AorD
srry if im wrong its not B because some of them are not compatible
Step-by-step explanation:
Answer:
<em> y = 4.25x</em>
Step-by-step explanation:
Given that:
After 2 week he has used 8 1/2 cups of dog food after 5 week he has used 21 1/4 cups, we can write this in coordinate form (x, y) where;
y is the amount of dog food
x is the time in weeks
The coordinates are (2, 8 1/2) and (5, 21 1/4)
get the slope m:
m = y2-y1/x2-x1
m = (21 1/4 - 8 1/2)/5-2
m = (85/4-17/2)/3
m = (85-34/4)/3
m = 51/12
m = 4.25
Get the intercept c:
Substitute any of the points say (2, 17/2) and m = 51/12 into the equation
y = mx+c
17/2 = 51/12(2) + c
17/2 = 51/6 + c
c = 17/2 - 51/6
c = 51-51/6
c = 0
Get the required equation:
substitute m - 4.25 and c = 0 into y = mx+c
y = 4.25x + 0
<em>Hence the required equation is y = 4.25x</em>
<em></em>