prove that
(z^a/z^b)^c * (z^b/z^c)^a * (z^c/z^a)^b =1

Answers

Answer 1

Step-by-step explanation:

remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.

when we have exponent of exponent, we multiply the exponents.

so,

the expression is

(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1

we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.

and therefore we have in there the terms :

z^ac / z^ac

z^bc / z^bc

z^ab / z^ab

all three are 1

and so the main expression is

1 × 1 × 1 = 1

which is true, of course, and therefore the original equation is true.


Related Questions

Driving 65 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 4 hours to get to her destination with the jet traveling at a speed of 400 mph. How many miles does Alicia travel to get to her destination?

Answers

Answer:

1,795 mi. traveled in total

Step-by-step explanation:

3 × 65 = 195 mi. driven by car

4 × 400 = 1,600 mi. flown by jet

1,600 + 195 = 1,795 mi. traveled in total.

What is the solution to a system with parallel lines?

Answers

Step-by-step explanation:

no solution because they never intercept

Find the circumference of the circle.
10 cm
The circumference is cm.
(Type an exact answer in terms of t.)

Answers

Answer:

the answer is either one or two answers

62.83 or 31.42

Step-by-step explanation:

This is the formula i used.

C=2πr

Circumference = 2·π·5 ≈ 31.41593 / 2·π·10 ≈ 62.83185

therefore,

t = 31.41593

      or

t = 62.83185

14) x - 27 0
3
X^3-27=0
X^3-27=0

Answers

Answer:

For the top equation, x = 27 (I think you meant to put x - 27 = 0. If not, I can always edit my answer for you)

For the bottom, x = 3

Hope this helps! Have a grrrreat day lol

Please help will give brainliest.

Answers

Answer:

D

Step-by-step explanation:

a is false since x could be 0.

b is easy to check, just plug numbers in, and we can see that it's false(you would get 0+0=1 and -0-0=-1 once plugged in)

c is also easy to check, just plot the line or simplify the first equation. since (2x+2y)/2=4/2 is also x+y=2, the second equation is also x+y=2, so it must have infinitely many solutions.

d must be true due to process of elimination but let's check to make sure.

7y=14x, divide both sides by 7 to get y=2x and since they're the same equation it must mean that they have infinitly many solutions and we can see that it is correct

6 grade math pls help and do step by step

Answers

Jay didnt follow the BEDMAS rule, he should have started withe the division because it has the priority based on the BEDMAS rule.

-3/4 × = 1/4 need Help to answer this question​

Answers

Answer:

x = -1/3

Step-by-step explanation:

step one - Simply both sides of the equation

step two - Multiply both side by 4/(-3)

I really need help please answer would help a lot

Answers

Answer:

z=13

Step-by-step explanation:

The sum of the two angles is 90 degrees

2z+5   + 5z-6  = 90

Combine like terms

7z-1 = 90

Add 1 to each side

7z-1+1 = 90+1

7z = 91

Divide each side by 7

7z/7 = 91/7

z =13

Answer:

5

Step-by-step explanation:

i had my teacher help me with I am on a one on one zoom

Please help me !!!!!!!!!

Answers

Answer:

f(-2) = 0

f(1) = 12

f(2) = 5

Step-by-step explanation:

f(-2) will lie in the function [tex] f(x) =x^2 - 4[/tex]

[tex]\therefore f( - 2) = {( - 2)}^{2} - 4 = 4 - 4 = 0 [/tex]

f(1) will lie in the function [tex] f(x) =2x^2 +10[/tex]

[tex]\therefore f(1) = 2 {(1)}^{2} + 10 = 2 + 10 = 12 [/tex]

f(2) will lie in the function [tex] f(x) =5[/tex]

[tex]\therefore f(2) = 5[/tex]

The spinner is divided into 4 equal parts: yellow (Y), green, (G), blue (B) and red (R). Dorian says that if you spin the spinner twice, then there are exactly 12 possible outcomes. he lists the outcomes in a table. Which statement explains Dorian’s mistake?

Answers

Answer:

The spinner can land on the same color twice in a row, so there should be 16 possible outcomes

Step-by-step explanation:

4 possible outcomes with the same color

RR, OO, GG and BB.

Total Ways = 12+4=16

The branch manager of an outlet (Store 1) of a nationwide

chain of pet supply stores wants to study characteristics of her

customers. In particular, she decides to focus on two variables: the

amount of money spent by customers and whether the customers

own only one dog, only one cat, or more than one dog and/or cat.

The results from a sample of 70 customers are as follows:

Amount of money spent: X = +21.34, S = +9.22.
Thirty-seven customers own only a dog.
Twenty-six customers own only a cat.
Seven customers own more than one dog and/or cat.
Construct a 95% confidence interval estimate for the
population mean amount spent in the pet supply store.

Construct a 90% confidence interval estimate for the population proportion of customers who own only a cat.
The branch manager of another outlet (Store 2) wishes to conduct

a similar survey in his store. The manager does not have access to

the information generated by the manager of Store 1. Answer the

following questions:

c. What sample size is needed to have 95% confidence of

estimating the population mean amount spent in this store

to within { +1.50 if the standard deviation is estimated to

be $10?

d. How many customers need to be selected to have 90% confidence of estimating the population proportion of customers who own only a cat to within {0.045?

e. Based on your answers to (c) and (d), how large a sample should the manager take?

Answers

Answer:

1. ( 19.1416, 23.5384,)

2. (0.276348, 0.46651)

3. the sample size = 170.73 approximately 171

4. sample size = 334.07 approximately 334

5. sample of 334 should be taken by manager

Step-by-step explanation:

mean = bar x = 21.34 dollars

size of sample n = 70

standard deviation of sample = 9.22

we use t distribution as the population standard deviation is not known.

95% Confidence interval

1-α = 0.95

α = 0.05

degree of freedom = 70-1 = 69

α/2 = 0.025

using the t distribution tsble,

= 1.9949

confidence interval = [tex]21.34+-1.9949*[\frac{9.22}{sqrt(70)}] \\[/tex]

= 21.34 +- (1.9949*1.10200)

= 21.34 + 2.1984, 21.34 - 2.1984

= (23.5384, 19.1416)

the confidence interval of the mean amount spent at the supply store can be written as 19.1416<u<23.5384

2. sixe of those who only have a cat

p = 26/70 = 0.371429

at 90 % confidence interval,

1-α = 0.90

α = 0.10

we use the z table here

z(0.10/2) = Z(0.05)

= 1.645

[tex]0.371429+-1.645\sqrt} \frac{0.371429(1-0.371429)}{70}[/tex]

= 0.371429 +-( 1.645 x 0.0578)

= 0.371429 + 0.095081, 0.371429 - 0.095081

= (0.276348, 0.46651)

3. sd = 10$

margin of erro,r e = 1.50$

α = 0.05

using z table

α/2 = Z0.025

= 1.96

sample size = 1.96² * 10² / 1.50²

= 3.8416 * 100/ 2.25

= 170.73

the sample size is approximately 171

d. we have 0.5 as sample proportion now

margin of error = 0.045

α = 0.10

Zα/2 = 0.05

= 1.645

sample size = 1.645²x0.5(1-0.5) / 0.045²

= 0.676506/0.002025

= 334. 07

sample size = 334

5.  sample of 334 should be taken by manager

23. Since 3 x 1/2 is the same as 1/2+ 1/2 +1/2 , what mixed number is the same
as 3 x 1/2?

Answers

Answer:

Step-by-step explanation:

3×1/2 = 1/2 + 1/2 + 1/2 = 3/2 = 1½

What is the equation of this line? ILL MARK BRAINLIST

A ~ y = -x + 2

b~ y = 2x -2

C ~ cannot be determined

D~ y = 2x + 2

Answers

This should be A. Hope this helps!

234235342421323254123+323546534311234

Answers

Answer:

I gotchu.

Step-by-step explanation:

234235342421323254123+323546534311234 = 2.34235666E20

Have a good day! :)

Si un vendedor gana $ 450 por cada venta de $ 50 000, ¿cuál es su tasa de comisión?​

Answers

Answer:

..?.?..............???............

BRAINLIEST + 25 POINTS
Part A: a^2 + 6 for a = 5

Part B: Show your work and/or explain how you arrived at your answer

Answers

Answer:

31

Step-by-step explanation:

Plug in 5 as a into the expression:

a² + 6

(5)² + 6

25 + 6

= 31

So, the answer is 31 when a = 5

substitute a=5 into the equation.

5²+6

25+6=31

hope that helps^^

Given the perimeter is 180cm what is the length and breadth of the rectangle?

Answers

Check out Kathy way tbh

Tripp swims 50 laps a day in
hopes of becoming a collegiate
swimmer. Write an equation to
represent y, the total number of
laps Tripp has swam after x
days.

Answers

Answer:

y = 50x

Step-by-step explanation:

how many solutions does 3-2x=5-x+3​

Answers

Answer:

x-2x=5+3-3

-x=5

x=-5

Step-by-step explanation:

That's the answer

3-2x = 5-x+3

First: Cancel 3 on both side

-2x =5-x

second: Add x to both side

-2x + x = 5-x + x

3rd: simplify -2x+x to -x

-x = 5

4rth: Multiply both side by -1

x = -5

there is one solution

If $9450 is invested at a rate of 12.5%,
compounded continuously, how much will it
be worth in 20 years?

Answers

Answer:

The final balance is $113,645.52.

The total compound interest is $104,195.52.

Step-by-step explanation:

What is the AREA of the given circle?
62.83 in²
157.08in²
314.16 in²
628.32 in²

Answers

Answer:

314.16 in²

Step-by-step explanation:

Answer:

[tex]A[/tex] ≈ [tex]314.16[/tex]

Step-by-step explanation:

[tex]A=\pi r^2[/tex]

[tex]A = \pi (10)^2[/tex]

[tex]A = \pi (100)[/tex]

[tex]A[/tex] ≈ [tex]314.16[/tex]

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?​

Answers

Answer:

Step-by-step explanation:

p

Step-by-step explanation:

Find the degree measure of each angle in the triangle.

Answers

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Please do not create new Amazon accounts until we verify your billing information. Any new orders that you place may be delayed or cancelled.

HELP!!! Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?

Answers

Answer:

He paid 9% in sales tax

Step-by-step explanation:

Help plzzz!! Marking most Brainly;)

Answers

Answer:

D it

Step-by-step explanation:

We have two equations, A quadratic and a linear equation.

The domain of a linear equation and quadratic equation is all real numbers but since it dealing with time we must make sure the roots or x-intercepts is positive.

Looking at the quadratic equation, we can use the discramnt formula to see if all roots are positve.

[tex]b {}^{2} - 4ac [/tex]

[tex] { - 6}^{2} - 4(1)(8.75)[/tex]

[tex]36 - 35 = 1[/tex]

The discramnt is greater than zero so there is two distinct real roots. So let check if they are positve

If you graph the equation, it intercepts at two positve roots so it is D

Complete each statement then state the property or properties illustrated by each statement on

Answers

Answer:

(8n)(-77)=-77(n*8)

We move all terms to the left:

(8n)(-77)-(-77(n*8))=0

We add all the numbers together, and all the variables

8n(-77)-(-77(+n*8))=0

We multiply parentheses

-616n-(-77(+n*8))=0

We calculate terms in parentheses: -(-77(+n*8)), so:

-77(+n*8)

We multiply parentheses

-616n

Back to the equation:

-(-616n)

We get rid of parentheses

-616n+616n=0

We add all the numbers together, and all the variables

=0

n=0/1

n=0

the property is Associative Property

Step-by-step explanation:

this one was kinda hard pls let me know it its right or not

Help!!!!
Given that slope = -4 and a point (-2,5), write an equation in standard form
of the line.

Answers

THE ANSWER IS: 4x+y=-3

first plug in the slope and given point into point-slope form

solve for y to get slope-intercept form

rewrite the equation in standard form

120
'N
A) 350
C) 135
D) 120

Answers

Answer:

it is d 120

Step-by-step explanation:

Benito runs 1/10 of a mile each day. which shows how to find the number of days it will take for benito to run 3/5 of a mile

Answers

I would say  divide 3/5 by 1/10

Michael is organizing a game of chance for his class. He asks each student to pick a ribbon from a bag and then put it back into the bag. The bag
has 12 yellow ribbons, 7 red ribbons, and 3 blue ribbons. If Jane picks a ribbon, what is the probability that the ribbon will be yellow and what is
the likelihood of this event?
OA. The probability is 1, and the event is certain.
OB. The probability is î and the event is likely.
OC. The probability is it and the event is unlikely.
OD The probability is it, and the event is neither likely nor unlikely.

Answers

Answer:

b

Step-by-step explanation:

Using the probability concept, it is found that the correct statement regarding the probability of picking a yellow ribbon is given by:

D The probability is of 0.5454 = 54.54%, and the event is neither likely nor unlikely.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 12 out of 22 ribbons are yellow, hence:

p = 12/22 = 6/11 = 0.5454 = 54.54.

The probability is greater than 0.05 but less than 0.95, hence it is neither likely nor unlikely, which means that option D is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ5

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