what laws of exponent they are:

1. (x-²)-³ = x⁶
2. (a^m)^n = a^m^n
3. a⁰ = 0

Answers

Answer 1

Answer:

The laws of exponents are:

a)  (x^n)*(x^m) = x^(n + m)

b)  (x^n)/(x^m) = x^(n - m)

c)  (x^n)^m = x^(n*m)

Now, let's see the given equations:

1) (x-²)-³ = x⁶   (true)

Here we se the third law, the "c"

(x^(-2))^(-3) = x^(-2*-3) = x^6

Then this equation is correct.

2)  (a^m)^n = a^m^n   (false)

This law does not exist, this is false.

An example of why this is false is:

Let's use the values:

a = 2, m = 1, and n = 2

then, in the left side we have:

(2^1)^2 = (2)^2 = 4

And in the right side we have:

2^(1^2) = 2^(1) = 2

We can see that we have different things in the left side than in the right side, then that relation is false.

3)  a⁰ = 0  (false)

Let's rewrite this as:

a^0 = a^(n - n)

Now we can use the second law to rewrite this as:

a^(n - n)  = (a^n)/(a^n)

And we have a number divided by the exact same number, we know that this is equal to 1, then:

(a^n)/(a^n) = 1

this means that:

a^0 = 1.

Then this is also false.

The only correct option is the first one.


Related Questions

Which is the graph of y -3= -2/3( x+ 6)?

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Answer:

y= −2/3x−1

Step-by-step explanation:

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The mean for this set of data is 18. Which number could be put in the blank to make this statement true?
16 10 22 ___
A. 84
B. 24
C. 48
D. 72

Answers

The answer is B, 24
Because if u do the math it will or should give u that

The mean of the data is 18 and the missing statement is x = 24

What is Mean?

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the data be represented as A

Now , the value of A = 16 , 10 , 22 , x

Let the mean of the data be M = 18

To find the mean of the data set, we need to add up all the numbers and divide by the total number of numbers:

(16 + 10 + 22 + x) / 4 = 18

We can simplify this equation by multiplying both sides by 4 to get rid of the fraction:

16 + 10 + 22 + x = 72

Now we can solve for x by subtracting the three known numbers from both sides:

x = 72 - 16 - 10 - 22

x = 24

Therefore, the number that could be put in the blank to make the statement true is 24

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If you can anserw both of them that’ll be great if not that’s okay too !! I need this as fast as possible thank you !!!!

Answers

Answer:

Step-by-step explanation:

Slope intercept formula: y = mx + b

m = slope

b = y-intercept

Substitute

14.) y = 1x + 0

Basically y = x

15.) y = 2x + (-7)

     y = 2x - 7

2 1/4w =6 3/4 answers pls hurry

Answers

Answer:

3

Step-by-step explanation:

3 * 2 1/4 = 6 3/4

I'm in need of assistance here, please answer ASAP!

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What u need help with?

Answer: where do you need assistance

Step-by-step explanation:

can someone pls help me with this!! ​

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Answer:

1st one

Step-by-step explanation:

The school's copier can
make 30 copies in 12a
minute. How many
copies can it make in 18
minutes?

Answers

Answer: 45 copies in 18 minutes

Step-by-step explanation:

i figured it out ;)

Write the ratio of ears to toes on an average person? (in simplest form)
type your answering using one of the following... (NO SPACES)
to

Answers

Answer:

1:5

Step-by-step explanation:

DivideByTwo

A, B, C, and D are the four angles of a parallelogram. a.Show that angle A = angle C
b.Show that angle B = angle D

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Answer:

look at the pictures

Step-by-step explanation:

HOPE THIS helps

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i think the answer is 2.8
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PLEASE HELP I HAVE TO TURN THIS IN SOON
In ∆XYZ, m∠X = 115°,m∠Y = 23°. What is m∠Z?

Answers

Answer:

X+Y+Z=180

115+23+Z=180

Z=180-115-23

Z=42°

Step-by-step explanation:

The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?

a3 – b3 = (a – b)(a2 + ab + b2)

A. (x – 4)(x2 + 4x + 8)
B. (x – 4)(x2 + 4x + 16)
C. (x – 64)(x2 + 64x + 16)
D. (x – 64)(x2 + 64x + 4,096)

Answers

Answer:

B

Step-by-step explanation:

(x - 4) because a = x and b = 4, subsitute into (a - b)

(x2 + 4x + 16) because if a = x and b = 4, you subsitute them into (a2 + ab + b2) to get your answer

Simplify the expression 2(5r + 8) - 4
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here’s your answer, 10(r+2)

I need this ASAP PLSS help

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Answer:

I think d.) 1

Step-by-step explanation:

1/2 and 3/4 is a 1/4 difference bc 1/2= 2/4

3/4 + 1/4 is a cup. I may be wrong

Answer:

1 1/8 cups

Step-by-step explanation:

ratio is x1.5

A cereal company is determining the nutritional information of a new recipe. They took a random sample of 20 servings of the cereal and measured
the number of calories in each serving. The number of calories in each serving are listed.
143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180
The box plot shown is a summary of the data. Move numbers to the spaces to label the values and complete the box plot.
143
180
not drawn to sale
145
150
151
160.5
160.7
165
166.5
177

Answers

Answer:

Minimum is 143, second whisker is 150, median is 160.5, 3rd quartile is 166.5, maximum is 180

Step-by-step explanation:

The first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5

How does a boxplot shows the  data points?

A box plot has 5 data description.

The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile)  has approx 75% in its left partition, and on its right lies approx 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

For this case, the data is:

143, 145, 147, 150, 150, 152, 157, 159, 160, 160, 161, 163, 164, 165, 165, 168, 173, 175, 177, 180

It is already sorted. There are 20 values.

We have to find the limits of box and the mid line, which are the three quartiles.

Dividing 20 in 4 equal parts give size of 5

Thus, 5-5-5-5 groups will be made by the three quartiles of this data.

The fifth value is 150, and sixth is 152. Any number between 150 and 152 can be taken as the first quartile, as before it will lie 25% of values and 75% of the data  after that value. By tradition, we take average of these two values, so its 151 as the first quartile of the considered data set.

In the similar way, the second quartile or median is mean of 10th and 11th value which evaluates to (160+161)/2 = 160.5

And, the third quartile is the mean of 15th  and 16th value of this data set, which evaluates to (165+168)/2 = 166.5

Thus, the first box is fillled with first quartile 151, the second box is filled with second quartile 160.5, and the third box is filled with the third quartile 166.5

Learn more about quartiles here:

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Answers pleasee this stuff is hard

Answers

Answer:

According to the integral root theorem the only possible real, integral zeros are +/- factors of (10*3 - 8)

... or factors of 992(+/-).  you can test by direct substitution.  No positive values are roots ... try 1, 1332, but as x increases so does y ...  so there are no positive roots.

  Roots, means y = 0 ...  so (x + 10)^3  = 8 ... take cube root ... x + 10 = 2  .. x = -8

x = -8 is a root

Testing other negatives and the y values are not zero but tend toward - infinity.

So the only real zero is x = -8

Answer:

it helps you

Step-by-step explanation:

this is for y = (x-10)^3 - 8

According to the integral root theorem the only possible real, integral zeros are +/- factors of (10*3 - 8)

... or factors of 992(+/-). you can test by direct substitution. No positive values are roots ... try 1, 1332, but as x increases so does y ... so there are no positive roots.

Roots, means y = 0 ... so (x + 10)^3 = 8 ... take cube root ... x + 10 = 2 .. x = -8

x = -8 is a root

Testing other negatives and the y values are not zero but tend toward - infinity.

So the only real zero is x = -8

Similarly for y = (x + 7)^3 +2 = 0

(x + 7)^3 = -2

x + 7 = cube root (-2)

x = -7 + cube root (-2) <<< the only real root

A runner's distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner's times has a z-score of –1.76. What is the runner's time?

Answers

Answer:

The runner’s time is 3.18 minutes

Step-by-step explanation:

Mathematically;

z-score = (x-mean)/SD

In this question, we have the z-score but we want to calculate x

From the question

z-score = -1.76

mean = 4.5 minutes

SD = 0.75 minutes

x = ?

Substituting these values, we have that

-1.76 = (x-4.5)/0.75

0.75(-1.76) = x - 4.5

-1.32 = x - 4.5

x = 4.5 -1.32

x = 3.18

Answer:

3.18

Step-by-step explanation:

edg

Jason’s current age is 1/4 his mom’s current age. In 16 years, Jason’s age will be 1/2 his mom’s age. The equation below can be used to determine x, Jason’s current age. What is Jason’s current age, in years

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Step-by-step explanation: if you download Math-way you’ll get a lot of answers I was doing a test and I seen u didn’t have an answer so I decided to help you

Use the system of equations to answer the question.
x + y = 3
y = x - 5
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Answers

Answer:

the answer to the system of equation is (4, -1)

Mike is purchasing fabric for a school project. He needs to cut out circles with an area of 314 square inches. The fabric at the store is precut into squares, each of which has a whole number of inches for the length of its side. What is the smallest square piece of fabric Mike can purchase to use to cut out one of the circles?​

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20 inches.............

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Answers

Answer:

a is ( 4,8) B is ( 6,5) and c is ( 2.3)

Step-by-step explanation:

Combine like terms to simplify the following expression : 12x+4y-3x+2-8y^2+9

Answers

8

2

+

9

+

4

+

1

1 fgdfgdfgdfgdfg

Factor the expression completely. 54 – 24x​

Answers

Answer:

6(9-4x)

Step-by-step explanation:

Factor 6 out of 54-24x, or group and factor out the GCF. Hope this helps!

Write an equation in the form ax? + bc+c=0 if the roots are r1= - 7 and r2 = -5

Answers

Answer:

A

Step-by-step explanation:

its A. bb cncnd shnans skajana. a

The 1985 Mexico City earthquake measured a magnitude 8.0 on the Richter scale. The Richter scale uses the function M (I) = log (StartFraction I Over I Subscript 0 Baseline EndFraction). Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io?

A.) I = 810(Io)

B.) Io = 810(I)

C.) I = 108(Io)

D.) Io = 108(I)

Answers

Answer:

The correct option is C: I = 10⁸I₀.   

Step-by-step explanation:

The function of the Richter scale is:

[tex] M_{(I)} = log(\frac{I}{I_{0}}) [/tex]

Since the magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, Io, is:

[tex] 8.0 = log(\frac{I}{I_{0}}) [/tex]

[tex] 10^{8} = \frac{I}{I_{0}} [/tex]

[tex] I = 10^{8}I_{0} [/tex]

Therefore, the correct option is C: I = 10⁸I₀.                

I hope it helps you!                    

The equation relates with the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, [tex]I_0[/tex] is [tex]I = 10^8I_0[/tex].

Given that,

The 1985 Mexico City earthquake measured a magnitude of 8.0 on the Richter scale.

The Richter scale uses the function M (I) = log (Start Fraction I Over I Subscript 0 Baseline End Fraction).

We have to determine,

Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io.

According to the question,

The function of the Richter scale is:

[tex]M_(_I_) =log[ \dfrac{I}{I_0}][/tex]

The magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, [tex]I_0[/tex] is:

[tex]M_(_I_) =log[ \dfrac{I}{I_0}]\\\\8 =log[ \dfrac{I}{I_0}][/tex]

Taking log base 10 both sides,

[tex]10^8 = \dfrac{I}{I_0}\\\\I = 10^8I_0[/tex]

Hence, The equation relates with the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, [tex]I_0[/tex] is [tex]I = 10^8I_0[/tex].

To know more about the Exponential function click the link given below.

https://brainly.com/question/15673235

Hi please help. i’ve been stuck on this for 5 minutes

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It’s 104. You have to add the sides and with that sum. You multiply by 4.

I need help with A,B and c

Answers

Step-by-step explanation:

a. D( as it has 7 sides)

b. D(as it has 7 sides)

c. B( as it has 9 sides)

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Answers

Answer:

216*64/8=1728....

Step-by-step explanation:

12³ is the appropriate answer

I WILL MARK THE BRAINEST

1.How many exterior angles are there at each vertex of the triangle

2.How many exterior angles does a triangle have in all

Answers

Answer:

blank 1: 2

blank2: 6

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