What are the 7 rules of exponents?

Answers

Answer 1

The 7 rules of exponents are:

Product Rule: When multiplying two numbers with the same base, add the exponents. For example, [tex]a^m * a^n = a^{(m+n)}[/tex]

Quotient Rule: When dividing two numbers with the same base, subtract the exponents. For example, [tex]a^m / a^n = a^{(m-n)}[/tex]

Power Rule: When raising a power to a power, multiply the exponents. For example, [tex](a^m)^n = a^{(m*n)}[/tex]

Zero Exponent Rule: Any non-zero number raised to the power of 0 is equal to 1. For example, [tex]a^0[/tex] = 1, where a is not equal to 0

Negative Exponent Rule: When a number is raised to a negative exponent, it is the same as the reciprocal of the number raised to the positive exponent. For example, [tex]a^{-n}[/tex] = 1/[tex]a^n[/tex]

One Exponent Rule: When a number is raised to the power of one, it stays the same. For example, [tex]a^1[/tex] = a

Zero Exponent Rule: Any number raised to the power of 0 is equal to 1. For example, [tex]a^0[/tex] = 1

It's worth noting that these rules are only valid for real numbers, with the exception of the zero exponent rule, which is valid for any number except for zero. Also, some rules may have restrictions such as the Negative exponent rule, where the base cannot be zero.

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Related Questions

What scale factor was applied to the first rectangle to get the resulting image?

Answers

Answer: Another way to look at it is that the rectangle was reduced in a factor of 5 (1/0.2=5)

don't forget to drop a heart hope it helped

Step-by-step explanation:

Answer: 1/0.2=5

Step-by-step explanation:

I hope this helps if you guys need a reach out to me :)

If 95% of students are coming to school tomorrow, what is the complement?

Question 5 options:

A. 95%


B. 100%


C. 1%


D. 5%

Answers

Answer:

d

Step-by-step explanation:

can you help me with this question According to Frost in his poem "The Road Not Taken," what kind of difference did taking one road over another road make? A. It made a good difference, B. It made a bad diference, c. Frost does not say

Answer:

the answer is d

Step-by-step explanation:

it only takes 5% to get to 100%

que volumen ocupará 600 g de agua?

Answers

Answer:

Step-by-step explanation:

600 ml

Well I need the help in this last question I will mark brain list if you got it right

Answers

Answer:

6x−11y+15

Step-by-step explanation:

Distribute the Negative Sign:

=5x−6y+7+−1(−x+5y−8)

=5x+−6y+7+−1(−x)+−1(5y)+(−1)(−8)

=5x+−6y+7+x+−5y+8

Combine Like Terms:

=5x+−6y+7+x+−5y+8

=(5x+x)+(−6y+−5y)+(7+8)

=6x+−11y+15

Answer:

6x−11y+15

I hope I helped!!

(5x-6y+7) -(-x +5y -8)
=5x-6y+7+x-5y+8
=6x -11y +15
Hope it helps you (^_^)

89+67
berapakah jawapan nya​

Answers

Answer:

156

Step-by-step explanation

fgcfgvhvcfgvxxbbhhcx

Answer:

Jawapan kepada 89 + 67 = 156

What is 631.051 as a fraction
sorry if that doesnt make sense.

Answers

Answer:

631 and 51/1000

Step-by-step explanation:

Please help me 15 points it’s worth it please help me on this question

Answers

Answer:

last answer

Step-by-step explanation:

a quadratic polynomial the sum of whose zeros is -3 and product is -10​

Answers

Answer:

2 and -5 i think

Step-by-step explanation:

How do you solve for x and y?

Answers

Answer:

x = 100, y = 50

Step-by-step explanation:

Make a system of equations:

First, you know that x + y degrees and 30 degrees are on a line together, they add up to 180 degrees:

x + y + 30 = 180

x + y = 150

Next, the interior angles of a triangle always add up to 180 degrees, and since 2y, x/2, and 30 are all the angles in a triangle, you have:

2y + x/2 + 30 = 180

x/2 + 2y = 150

Now, all you have to do is solve the system of equations.

To start, multiply the second equation by 2 to get rid of the fraction:

x + 4y = 300

Then, you can subtract the two equations:

x + 4y = 300

- (x + y = 150)

3y = 150

divide both sides by 3

y = 50

substitute y = 50 into the equation x + y = 150:

x + 50 = 150

x = 100

Josie makes invitations for her aunt's paper company. Of all the invitations Josie makes, 15/21 are children's party invitations. Of those invitations, 3/5 have an animal on them. What fraction of the invitations Josie makes are children's party invitations with an animal on them?

Answers

Answer:

the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

The computation of the fraction of the invitations considered to be an animal on them is shown below:

= Children party invitations × animal on them

[tex]= \frac{15}{21} \times \frac{3}{5}\\\\= \frac{3}{7}[/tex]

Hence, the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]

GIVING BRAINLIEST!!!

Answers

Answer:

i think its 78.5 but the answers not on there the closest one there to it is 76.5 so just put that one

Step-by-step explanation:

tysmmmmmmmmmmmmmmmmmmmmmm

Answers

Answer:

The answer is 10

Step-by-step explanation:

To get this you will make the improper fraction into a fraction and then turn that into decimal form

[tex]4 \frac{1}{8} = 4[/tex]

and

[tex]5 \frac{6}{10} = 6[/tex]

That is how you find the estimated answer

Hope this Helped

can someone please help me u can just do 5 and explain please


¿Puede alguien ayudarme? Puedes hacer 5 y explicar por favor.

Answers

Answer:

i only can explain until number 7

i am sorry

maybe that help you

Please help! image is shown below

Answers

Answer:

I think 3 maybe since 5 times 3 is 15

Step-by-step explanation:

Answer:

z=10

Step-by-step explanation:

60/40=1.5

15/1.5=10

Christine has her own dog -walking business. She Charges her customers $20 per day to walk their day

Answers

Answer:

y= money made

x = amount of dogs walked

equation- y = 20x

for the table name # of dogs walked on the right and money earned on the left.

for the left put 1 2 3 4 5 6 7 and 8

1 goes with 20

2 goes with 40

3 with 60

4 with 80

5 with 100

6 with 120

7 with 140 and

8 with 160

Step-by-step explanation:

PLEASE I NEWD HELP ON THIS

Answers

Answer:

5. Inequality form: n  ≥  3

   Interval notation: [3, ∞)

       

6.  Inequality form: x < 4

    Interval notation: (- ∞, 4)                          

11. Inequality form: x > 50

   Interval notation: (50, ∞)

12. Inequality form: y [tex]\geq[/tex] 8

     Interval notation: [8, ∞)

15. Inequality form: z < 8

    Interval notation: (- ∞, 8)

       

16. Inequality form: y [tex]\geq[/tex] 4

    Interval notation: [4, ∞)

Step-by-step explanation:

I tried to graph them as best as I could, I hope this helps!

What is the scientific notation for .000472

Answers

Answer:

The scientific notation for 0.000472 is 4.72 * [tex]10^{-4}[/tex].

Delia takes out a loan to buy a car for $18,000 with an interest rate of 6.5%. The amount of interest Delia will have to pay is $4,680. Write and solve an equation to determine the number of months her loan is for. Show all of your work and explain how you got your number of months.

Answers

Answer:

Delia pays $4,680 in 4 months

Step-by-step explanation:

Equation:

18,000 * 6.5% = 1170

4680 ÷ 4 = 1170

So, the answer is 4 months this is the equation.

Hope this helps! :)

Hi! PLS HELP ITS 30 POINTS!! Thanks!
A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?

15 millimeters
150 millimeters
1,500 millimeters
15,000 millimeters
Pls help!
Imma report u if its something off the topic!
Thanks again!
(its not b i tried it and got it wrong!! )

Answers

Answer:

1,500 millimeters

Step-by-step explanation:

1 litre = 1000 millilitre.

Try 1,500.

pls help ty !
question is in the pic

Answers

Yes the answer is correct because you are adding 2 perfect squares and you get the same answer !

Answer:

He is not correct

The altitude of an airplane is decreasing at a rate of 40 feet per second. What is the change in altitude of the airplane over a period of 20 seconds?

Answers

Answer:

Step-by-step explanation:

-40t

-40(20)

-800 ft

Can someone please tell me what is the solution

Answers

Answer:

[tex] \frac{1}{4} \tan {}^{4}(x) + c[/tex]

Find (3x+1)(x+4) using the table of products. Write your answer in standard form.

Answers

Step-by-step explanation:

just multiply both the values and get the quadratic solution.

The standard form of the (3x+1)(x+4) is 3x^2+13x+4=0.

We have given that,

(3x+1)(x+4) using the table of products.

We have to determine the standard form.

What is the formula of the standard form?

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

ax^2+bx+C=0

[tex]=3xx+3x\cdot \:4+1\cdot \:x+1\cdot \:4[/tex]

[tex]=3x^2+13x+4[/tex]

Therefore the standard form is 3x^2+13x+4=0.

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HELP PLEASE !! URGENT !!

Answers

Directions and I am not sure of the other answer sorry :)

E = MV^2 ÷ 2 + mgh, Make V Subject of the formula​

Answers

Answer:

[tex] \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]

Step-by-step explanation:

[tex]E = MV^2 ÷ 2 + mgh \\ \\ E - mgh = MV^2 ÷ 2 \\ \\ 2(E - mgh)= MV^2 \\ \\ \frac{2(E - mgh)}{M}=V^2 \\ \\ \sqrt{\frac{2(E - mgh)}{M}} = V \\ \\ \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]

10.
Write a rule for the linear function in the graph.

A. y = 4/5x + 2

B. y = -5x - 2

C. y = 5/4x - 2

D. y = -4/5x + 2

Answers

Answer:

D. y = -4/5x + 2

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope:  

4

5

y-intercept:  

(

0

,

2

)

x

y

0

2

5

2

0

Find the volume of the figure.
10 cm
8 cm
10 cm
14 cm
10 cm
8 cm
cubic centimeters

Answers

Answer:

60 cm³

Step-by-step explanation:

Step-by-step explanation:

=896000 is the answer

method -10x8x10x14x10x8

️️

4. Six numbers are shown.
1.25, -1.5, -0.75,
34,
2 6/8,
5/4
Place each number in its correct location on the number line.

Answers

Step-by-step explanation:

sorry i couldn't solve the last and the last second one

Was it helpful?

comment down

If there is any kind of suspicious mistake

then sorry

Please help it’s due in 20 mins would it be A B C or D

Answers

Option C is correct

x < 1

Answer:

C ) x < 1

Step-by-step explanation:

The open circle on a number line means: less than or greater than. The arrow is pointing to the left, towards the negatives, so x would be less than 1.

Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)

Answers

Answer:

B (5, 13)

Step-by-step explanation:

9x + 4y = 97

9x + 6y = 123

To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.

First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.

-1(9x + 6y = 123)

-9x - 6y = -123

This is one of your equations. Set it up with your other given equation.

9x + 4y = 97

-9x - 6y = -123

Imagine this is one equation. Since every term is negative, you will be subtracting each term.

9x + 4y = 97

-9x - 6y = -123

___________

0x -2y = -26

-2y = -26

To isolate y further, divide both sides by -2.

y = 13

Now, to find x, plug y back into one of the original equations.

9x + 4(13) = 97

Multiply.

9x + 52 = 97

Subtract.

9x = 45

Divide.

x = 5

Check your answer by plugging both variables into the equation you have not used yet.

-9(5) - 6(13) = -123

-45 - 78 = -123

-123 = -123

Your answer is correct!

(5, 13)

Hope this helps!

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