Answer:
- b/a
- 16a²b²
- n¹⁰/(16m⁶)
- y⁸/x¹⁰
- m⁷n³n/m
Step-by-step explanation:
These problems make use of three rules of exponents:
![a^ba^c=a^{b+c}\\\\(a^b)^c=a^{bc}\\\\a^{-b}=\dfrac{1}{a^b} \quad\text{or} \quad a^b=\dfrac{1}{a^{-b}}](https://tex.z-dn.net/?f=a%5Eba%5Ec%3Da%5E%7Bb%2Bc%7D%5C%5C%5C%5C%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%5C%5Ca%5E%7B-b%7D%3D%5Cdfrac%7B1%7D%7Ba%5Eb%7D%20%5Cquad%5Ctext%7Bor%7D%20%5Cquad%20a%5Eb%3D%5Cdfrac%7B1%7D%7Ba%5E%7B-b%7D%7D)
In general, you can work the problem by using these rules to compute the exponents of each of the variables (or constants), then arrange the expression so all exponents are positive. (The last problem is slightly different.)
__
1. There are no "a" variables in the numerator, and the denominator "a" has a positive exponent (1), so we can leave it alone. The exponent of "b" is the difference of numerator and denominator exponents, according to the above rules.
![\dfrac{b^{-2}}{ab^{-3}}=\dfrac{b^{-2-(-3)}}{a}=\dfrac{b}{a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bb%5E%7B-2%7D%7D%7Bab%5E%7B-3%7D%7D%3D%5Cdfrac%7Bb%5E%7B-2-%28-3%29%7D%7D%7Ba%7D%3D%5Cdfrac%7Bb%7D%7Ba%7D)
__
2. 1 to any power is still 1. The outer exponent can be "distributed" to each of the terms inside parentheses, then exponents can be made positive by shifting from denominator to numerator.
![\left(\dfrac{1}{4ab}\right)^{-2}=\dfrac{1}{4^{-2}a^{-2}b^{-2}}=16a^2b^2](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B1%7D%7B4ab%7D%5Cright%29%5E%7B-2%7D%3D%5Cdfrac%7B1%7D%7B4%5E%7B-2%7Da%5E%7B-2%7Db%5E%7B-2%7D%7D%3D16a%5E2b%5E2)
__
3. One way to work this one is to simplify the inside of the parentheses before applying the outside exponent.
![\left(\dfrac{4mn}{m^{-2}n^6}\right)^{-2}=\left(4m^{1-(-2)}n^{1-6}}\right)^{-2}=\left(4m^3n^{-5}}\right)^{-2}\\\\=4^{-2}m^{-6}n^{10}=\dfrac{n^{10}}{16m^6}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B4mn%7D%7Bm%5E%7B-2%7Dn%5E6%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E%7B1-%28-2%29%7Dn%5E%7B1-6%7D%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%284m%5E3n%5E%7B-5%7D%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3D4%5E%7B-2%7Dm%5E%7B-6%7Dn%5E%7B10%7D%3D%5Cdfrac%7Bn%5E%7B10%7D%7D%7B16m%5E6%7D)
__
4. This works the same way the previous problem does.
![\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}=\left(x^{-4-(-9)}y^{1-5}\right)^{-2}=\left(x^{5}y^{-4}\right)^{-2}\\\\=x^{-10}y^{8}=\dfrac{y^8}{x^{10}}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7Bx%5E%7B-4%7Dy%7D%7Bx%5E%7B-9%7Dy%5E5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B-4-%28-9%29%7Dy%5E%7B1-5%7D%5Cright%29%5E%7B-2%7D%3D%5Cleft%28x%5E%7B5%7Dy%5E%7B-4%7D%5Cright%29%5E%7B-2%7D%5C%5C%5C%5C%3Dx%5E%7B-10%7Dy%5E%7B8%7D%3D%5Cdfrac%7By%5E8%7D%7Bx%5E%7B10%7D%7D)
__
5. In this problem, you're only asked to eliminate the one negative exponent. That is done by moving the factor to the numerator, changing the sign of the exponent.
![\dfrac{m^7n^3}{mn^{-1}}=\dfrac{m^7n^3n}{m}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm%5E7n%5E3%7D%7Bmn%5E%7B-1%7D%7D%3D%5Cdfrac%7Bm%5E7n%5E3n%7D%7Bm%7D)
Answer:
5
Step-by-step explanation:
the slope is the number behind the x in this type of equation
Answer:
5/4 kg is Parcel A
im guessing what you meant was that parcel B is 3 times as heavy as A.
Step-by-step explanation:
Lets say parcel A is x
3x would be parcel b
x + 3x = 5 kg
4x = 5 kg
x = 5/4 kg
Answer:
<u>In a right angled triangle, the sine of an angle is: The length of the side opposite the angle divided by the length of the hypotenuse. </u>
<u>The abbreviation is sin. sin θ = opposite / hypotenuse.</u><u>2 cosA sinB = sin(A + B) − sin(A − B) 2 cosA cosB = cos(A + B) + cos(A − B) 2 sinA sinB = cos(A − B) − cos(A + B)</u>
Step-by-step explanation:
hi sushant
for another definition:-
Shina (word), or Sina (Japanese: 支那) means archaic Japanese word for China.
Answer: She can buy 6 shirts
Step-by-step explanation: You subtract 95 from 240, which gives you 145 so you do 145/22.5 which will give you 6.4444 but you can't buy .44 of a shirt so you round down and you get 6.