DESCRIBE how a power with a zero exponent (a^0) and a power with a negative exponent (a^−n) can be simplified.

Answers

Answer 1

Answer:

[tex]a^{-n}[/tex] is [tex](\frac{1}{a})^{n}[/tex] OR [tex]\frac{1}{a^{n} }[/tex]

[tex]a^{0}[/tex] = 1, where a ≠ 0

Step-by-step explanation:

To simplify the exponents, you must put it in positive value

Example:

The simplest form of [tex]2^{-3}[/tex] is to change the exponent from negative value to positive value.

You can do that by reciprocal the number, [tex]2^{-3}=(\frac{1}{2})^{3}[/tex]You can write it [tex]\frac{1}{2^{3}}[/tex], because 1 to any power equal 1

That means if you want to simplify [tex]a^{-n}[/tex], reciprocal a and change the sign of the power from -n to n

The simplest form of [tex]a^{-n}[/tex] is [tex](\frac{1}{a})^{n}[/tex] OR [tex]\frac{1}{a^{n} }[/tex]

For any number, a (a ≠ 0), 1 × a = a, so, the reason that any number to the zero power is 1 because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, (1)

Example:

The value of [tex](5)^{0}[/tex] = 1, because it is the product of no numbers, so it is equal to the multiplicative identity (1)

That means [tex]a^{0}[/tex] = 1, where a ≠ 0

Very important note:

[tex](0)^{0}[/tex] is undefined value


Related Questions

320÷b∙20 and 320÷(b∙20) for b=4

Answers

Answer:

Step-by-4vttbrbwtetbb4tbtb44tny4ny4nyn4tbryn4y

step explanation:

Whats the slope if this line??

Answers

Answer:

-1/4

Step-by-step explanation:

because its going up one over 4 and the lines negative!

Answer:

-1/4

Step-by-step explanation:

The slope is going down towards the right so it's negative. Rise-1 and you Run-4 so the answer is -1/4. Hope this helps :)

What is the pyhtagoream thereom and how can you use it to slove right triangles

Answers

Answer:

Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

a is one leg of the right triangle.

b is another left of the right triangle.

c is the hypotenuse of the right triangle.

We use the Pythagorean Theorem to help us solve for missing side lengths of a right triangle.

Filling up a tank of gas costs $36.96. If the tank holds 16.5 gallons of gas, then how much d
each gallon cost?

Answers

Answer:

$2.24 per Gallon

Step-by-step explanation:

36.96 divided by 16.5 is 2.24, then to check that multiple 2.24 by 16.5 and you get the total cost of 36.96. Hope this helps.

WILL MARK BRAINLIEST PLZ ANSWER FAST GUYS AND GIRLS. Don't mind the second question. You can answer it if you want that will help me.

Answers

Answer:

1. 10d + 5n = 85

2. look at graph  or graph coordinates (0, 17) and (8.5, 0) and make a line through them

3. 17 nickels since its only nickels, on the graph you see where the line hits the y-axis which is 17.

4. 8.5 dimes since its only dimes, on the graph you see where the line meets the x-axis which is 8.5

Step-by-step explanation:

y-axis is nickels

x-axis is dimes

A student worked out an equation and below is his solution. is the answer correct? If not, where was the error and what is the correct answer?
-4(6-r)=12
-24-4R=12
-4R=36
R=-9

Answers

Answer:

His answer is wrong.

Step-by-step explanation:

-4(6-R)=12  <-- Since R is negative, -4 times -R results in a positive so, 4R.

-24+4R=12

+24       +24

--------------------

4R = 36

R= 9

.4 ÷ 28.08 Dividing Decimals , Divide to the nearest Tenth??
I Will Give You 10 Points

Answers

Answer:

0

Step-by-step explanation:

The answer is 0.01424, but if you round it to the nearest tenth, you would end up with 0.

how do you solve u = 3a/2 solving for a

Answers

Answer:

Step-by-step explanation:

a=2a/3. ✌️

The answer that I got is 2a/3

Please help I need to get this answered!

Answers

Answer:

4  1/9

Step-by-step explanation:

so if we make the fraction the same having 7 4/9 and 3 1/3

we would then make 1/3 into 3/9 (its the smae thing not simplified)

subtract 7-3=4

4-3=1

and then simplify the fraction

The exact form would be 37/9
But in mixed number form, it would be 4 1/9

Lincoln Cook has a check for $295.50 and a check for $6.25. He also has a $10.00 bill
He would like to receive $5.00 in cash and deposit the rest of the money in his say-
ings account. What is the total deposit?

Answers

Step-by-step explanation:

First, we need to add all the checks and money he has.

295.50

 10.00

   6.25

+________

  3   6  1  . 7 5

Total- $361.75

Now, we have to subtract 5 from this.

361.75

   5.00

-______

3 5 6 . 7 5

The total deposit is $356.75

Answer:

$306.75 is the right answer i just took the test.

Step-by-step explanation:

#6 What integers describes overdrawing your bank account by $50?​

Answers

Answer:

-50

Step-by-step explanation:

A negitive number would mean debt or owed. A positive number would be a credit of a number.

Twice a number increased by 4 is at least 10 more than the number

Answers

Answer:

the twice as number increased by 4 is at least 10 more than a number .

2x + 4 ≥ x + 10

x ≥ 6

Step-by-step explanation:

Mark Brainliest

Answer:

2n+4 >= 10 + n

Step-by-step explanation:

solve for n , but remember the rules of dealing with inaqualities

Solve the equation given
x = - 4.
5 = x + 9

Answers

Answer:

x=-4

Step-by-step explanation:

You wrote the answer in the question, so there is really no question.

How it helps :)

hey guys can you answer this one question real quick

Answers

Answer:

a. 1/5

b. (3, 3/5)

c. 1/5x = y

Step-by-step explanation:

Remember: (x, y)

0.5 = 1/2

(1/2, 1/10) = 1/10 ÷ 1/2 = 1/10 • 2 = 1/5, you can divide y/x = constant of proportionality. 1/10 ÷ 1/2.

1 2/5 = 7/5

(7, 7/5) = 7/5 ÷ 7 = 7/5 • 1/7 = 1/5, y/x = constant of proportionality. 7/5 ÷ 7.

a. 1/5 is the constant of proportionalityb. (3, 3/5) because 3/5 ÷ 3 or 3/5 • 1/3 = 1/5.c. 1/5x = y

15 points!
What is the correct answer for Claire's problem? Explain where she went wrong.

Answers

Answer:

it would be y=50+25x

Step-by-step explanation:

There is an extra $25 per room, and since we dont know how many rooms she has cleaned, we can use x to represent that amount. So for x amount of rooms, it will be an extra $25

Help THIS IS DUE IN LESS THAN A HOUR

Answers

Take that back, please delete this question.

Answer:

i beleive its b or d

Step-by-step explanation:

mostly b


P(5. - 5), y=3x+3
Write an equation for the line in point-slope form

Answers

Answer:

M= 3

Step-by-step explanation:

l2ecdnienofnweucon fuovnewdionsdv wqueijncqodi

Answer:

y+5 =3(x-5)

Step-by-step explanation:

The point slope form of an equation is : y-y₁ = m(x-x₁)

Given in the question ;

x₁= 5

y₁ = -5

y= 3x+3 where m=3

The equation is :

y-y₁ = m(x-x₁)

y--5 =3(x-5)

y+5 =3(x-5) ----equation of the line in point-slope form.

Why does the base matter when simplifying negative exponents?

Answers

Answer:

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x–2" (pronounced as "ecks to the minus two") just means "x2, but underneath, as in 1 x 2 \frac{1}{x^2} x21 ".

Step-by-step explanation:

Help it’s homework!!!!

Answers

Answer:

(3x - 3)(x + 2)

Step-by-step explanation:

3x^2 + 3x - 6

(3x^2 + 6x)(-3x - 6)

3x(x + 2) -3(x + 2)

(3x - 3)(x + 2)

Please PLEASE help with these two math problems

1. 7^x ÷ 7^y =
2. z^10x^y ÷ z^5 =

Answers

Answer:

14

-25/1

Step-by-step explanation:

What strategy would be the best to solve this problem? Ann-Marie bought apples. She kept one-third for herself and gave the rest to 4 friends. Each friend got 2 apples. How many apples did Ann-Marie buy? A. guess, check and revise B. work backwards C. use a formula D. look for patterns

Answers

Answer:

D. Look for patterns

Step-by-step explanation:

To solve :

Assume number of apples bought = x

Fraction kept = 1/3 of x

Fraction shared = (x - x/3) = (3x - x) /3 = 2x/3

Number of people who shared (2x/3) = 4 with each getting 2

Total number shared = 4 * 2 = 8

Fraction shared = total shared

2x/3 = 8

Multiply both sides by 3

(2x/3) * 3 = 8 * 3

2x = 24

x = 12

Hence, Anne-Marie purchased 12 apples

You are going on a field trip and need to choose where to go, The zoo charges a $100 fee plus $10 per student. The museum charges $200 plus $5 per student. How many students have to go on the trip to make the museum a better deal

Answers

Answer:

21 kids have to go on the trip to make the museum a better deal

Step-by-step explanation:

Zoo: y=10x+100

Museum: y=5x+200

10x+100=5x+200

5x=100

x=20

When 20 kids go on trip the costs will be the same. Therefore, once 21 kids go the museum will be cheaper then the zoo as it is increasing at a rate of 5 dollars

solve.
5-(x-6)=-7+3(-x+2)

Answers

Answer:

x=-6

Step-by-step explanation:

For this equation, when we remove the parenthesis, we get 5-x+6=-7+-3x+6.

Then we simplify both sides of the equation, so we get 11-x=-1-3x. When we separate the numbers and variables, we get -12=-2x. -12/2 = -6.

5-x+6=-7-3x+6
combine like terma
11-x=-1-3x
add 3x to both sides
11+2x=-1
subtract 11 from both sides
2x=-12
x=-6

Solve [X + 8) = 5
With steps

Answers

Answer:

X=(-3)

Step-by-step explanation:

1.Subtract 8 from both sides of the equation.-(x+0)=5-8-the 0 is there because the 8 on the left side is canceled out.

2.5-8 is all you have to look at.-when you look at this you know that it will be negative because 8 is on the right of the minus sign and it is greater than 5.

3.Use a calculator or you fingers to find answer.-(4,3,2,1,0,-1,-2,-3)

HOPE THIS HELPS!!!

Find the equation of the line that passes through (2,8) and (6,48)

Answers

Answer: m = 10

.........................

What is the value of the expression (x – 2y) (x + 2y) when x= 4 and y=1/2

Answers

Answer:

15

Step-by-step explanation:

First you would plug in the 4 and 1/2 in the x and y's places, making the expression (4 - 2 (1/2))*(4 + 2 (1/2). Then you solve (below).

(4 - 2 (1/2))*(4 + 2 (1/2)

(4 - 1)*(4 + 1)

(3)*(5)

15

Hope this helped! If you have any questions, feel free to message me :)

Help please
And thank you so much

Answers

Answer:

$0.1 /lb.

Step-by-step explanation:

First, divide 1.99 by 19. You get 0.1047368421. To round it to the nearest hundred, look to the number 3 points away from the decimal, which is number 4. Since it is not 5 or greater, we round it down, and it would round down to 0.1.

25-2z-10z=-3(4z+8)-1
solve and how many solutions ?

Answers

distribute first
25-2z-10z=-12z-24-1
combine like terms
25-12z=-12z-25
add 12z to both sides
25=-25
no solution because the right side has a negative

Answer:

No Solutions

Step-by-step explanation:

Step 1:

25 - 2z - 10z = - 3 ( 4z + 8 ) - 1       Equation/Given

Step 2:

25 - 12z = - 12z - 25        Combine Like Terms/Multiply

Step 3:

25 = - 25       Add 12z on both sides

Answer:

No Solutions

Hope This Helps :)

What is the y intercept of this graph?. What is the slope?

Answers

Answer:

y intercept is -3

slope is 4

y=4x-3

Step-by-step explanation:

1/3 kilograms 2/3 what is the unit rate

Answers

Idk I download this app so other ppl can help me
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