1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
3241004551 [841]
3 years ago
11

Which is the simplified form of the expression

Mathematics
1 answer:
Elina [12.6K]3 years ago
5 0

Answer:

\displaystyle A=\frac{  4 }{ x^{14} y^{8}}

Step-by-step explanation:

<u>Properties of Powers</u>

The algebraic expression called power has the form  x^y where x is called the base and y is called the exponent.

Powers have some properties, some of which we'll recall below

(x^a)^b=x^{ab}

(x^a)(x^b)=x^{a+b}

\displaystyle \frac{x^a}{x^b}=x^{a-b}

\displaystyle x^{-a}=\frac{1}{x^a}

\displaystyle x^{a}=\frac{1}{x^{-a}}

We'll use those properties to simplify the expression

\displaystyle A=\left( \frac{ (2)^{-3}(x^{-3}) (y^2) }{(4^{-2}) (x^4) (y^6)} \right)^2

Taking the power 2 of every term

\displaystyle A=\frac{ (2)^{-6}(x^{-6}) (y^4) }{(4^{-4}) (x^8) (y^{12})}

Moving the terms with negative exponent to its opposite side

\displaystyle A=\frac{ (2)^{-6} (4^{4})(y^4) }{ (x^8)(x^{6}) (y^{12})}

Operating the explicit same bases

\displaystyle A=\frac{ (2)^{-6} (4^{4}) }{ (x^{14}) (y^{12-4})}

Since 4^4=(2^2)^4=2^8

\displaystyle A=\frac{ (2)^{-6} (2^8) }{ (x^{14}) (y^{12-4})}

Operating the remaining like bases subtractions

\displaystyle A=\frac{  (2^2) }{ (x^{14}) (y^{8})}

Finally

\displaystyle A=\frac{  4 }{ x^{14} y^{8}}

You might be interested in
If 1 qt = 2 cups how many cups are in 32 qt
tiny-mole [99]

Nvm

Step-by-step explanation:

8 0
3 years ago
2. What is the rule for this input-output table?
qwelly [4]

Answer:

First, this table is a function because it has no repeating input values

Second, it is increasing in both the x and y

third, since it is increasing in x and y it is a positive correlation( I dont know if you have learned that yet)

Fourth, the output increases by 4 each time the input increases by 1

Step-by-step explanation:

5 0
4 years ago
The scatter plot shows the amount of sleep Aria got the night before a test and her test scores. Which is the best prediction fo
xenn [34]

Answer:

its d gee

Step-by-step explanation:

good luck my firesn

7 0
3 years ago
Make an equation for the area of each rectangle.Solve it to find the value of x. Area=70cm^2 l=(2x+8)cm b=5cm​
Inessa05 [86]

Answer:

I gc bj jiu I'll vuhv jo b DDT UK k

3 0
3 years ago
A used boat is on sale for $1,800. Austin makes an offer equal to 2/3 of this price. How much does Austin offer for the boat? $6
blondinia [14]
1,200 for the boat because 1800 divided by 3 is 600 and times that by two because its 2/3 and then u get your answer of 1,200$
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is 858 divided <br> by 57
    14·2 answers
  • What is the initial value?
    13·1 answer
  • Find the missing lengths of the sides. b = , c = 16 b = , c = b = , c = b = , c = 12
    5·2 answers
  • Six less than the product of 4 and a number is equal to 2
    15·2 answers
  • 4. There are 10 cheerleading squads performing in a competition. The
    7·1 answer
  • Rose is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 8 meters away
    6·1 answer
  • Simplify each expression.<br> 12x+y4<br> (2x)(3x^3y8)
    5·1 answer
  • PLEASE HURRY IM BEING TIMED
    14·1 answer
  • I just need yall help ... {:
    12·2 answers
  • 2.61 X 4.3 whats the answer?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!