Simplify this expression.
[tex]\frac{4^{9} }{4^{3} }[/tex]

Answers

Answer 1

9x9x9x9divide by 4x4x4

Answer 2

Answer:

4⁹ / 4³ = 4⁶ = 4096

Step-by-step explanation:

You can solve this by realising that exponents (the 9 and the 3 in this case), simply tell you how many times to multiply the numbers together.

What you're see there then can also be expressed as:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}[/tex]

Because the numerator and denominator are all multiples of the same number repeatedly, you can simply eliminate the bottom three fours from the top and bottom, giving you:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times (4 \times 4 \times 4)}{(4 \times 4 \times 4)}\\\\= 4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

[tex]4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

A simpler way to look at it is to understand that when the same number is being raised to different bases, and then multiplied or divided, you can simply add or subtract the exponents.  For example, speaking very generically:

[tex]x^a \times x^b = x^{a + b}[/tex]

and

[tex]x^a \div x^b = x^{a - b}[/tex]

In this case then, we can simply say:

[tex]\frac{4^9}{4^3} = 4^{9 - 3} = 4^6[/tex]

So when simplified, the expression is equal to 4⁶, or 4096.


Related Questions

Change 8 a.m. to 24 hour clock time.
Use a colon : to separate hours and minutes

Answers

Answer:

08:00

Step-by-step explanation:

Answer:

8:00

Step-by-step explanation:

12/midnight would be 00:00 so 8am would be 8:00. if it were 8pm it would be 20:00

I GIVVVVEEE BRAINLILST I NEED HELPP

Answers

Answer:

The answer is J,

it can't be H because that would increase the size by 10, when the problem describes a reduction. and it cant be F or G because it has the x and y values in the wrong spots.

Step-by-step explanation:

I hope this helped :)

Which is the best estimate of 162% of 79? O 112 O 119 O 128 O 136​

Answers

Answer:

128

Step-by-step explanation:

You would multiply 79 by 1.62 to get the answer.

This would give you 127.98 which you would round up to 128.

Answer:

128

Step-by-step explanation:

What is the (fg)(x) if
f(x)=(4x - 1) and g(x)=(3x + 5)?
A. 7x + 4
B. 12x2-5
C. 12x2 + 17x-5
D. 12x2 + 23x - 5


Show work

Answers

(4x - 1)(3x + 5)

12x^2 + 20x - 3x -5

12x^2 + 17x -5

The answer is C.


5
12
of the pupils in Year 9 say their favourite colour is red.
There are 180 pupils in Year 9.
How many students said red is their favourite colour?

Answers

Red

⁣           
    
    

Doing my homework!
✏️✏️✏️✏️

Solve this pls. Thank you

Answers

Answer:

which one????????????????????

Another way to find slope is with the slope formula (y2-y1/x2-x1 find the slope of (3,2) (7,4)

Answers

Answer: 2/4=1/2

Step-by-step explanation: 4-2=2. 7-3=4

Answer:

1/2

Step-by-step explanation:

4-2=2

7-3=4

2/4

-2+(-7)= What is the answer? HELP!!!!!!!!!

Answers

Answer:

-9

Step-by-step explanation:

- 2 + ( - 7 )

- 2 - 7 = -9 ( Answer)

Jake says that there should be a decimal point in the quotient 142.45 ÷ 7.4 = 1,925 after the 2.

Part A
Which equation shows the best estimate for the quotient?
A. 150 ÷ 10 = 15
B. 150 ÷ 5 = 30
C. 140 ÷ 10 = 14
D. 140 ÷ 7 = 20
Part B
Use the drop-down menus to explain whether Jake is correct.
Jake
Choose...
correct because 192.5
Choose...
close to the estimate. The decimal point belongs after the
Choose...
.

Answers

Answer:

ok

Step-by-step explanation:

A circular light fixture has a radius of 20 centimeters.what is the circumference of the light fixture

Answers

Answer:

[tex]\boxed {\boxed {\sf 40 \pi \ cm, 125.6 \ cm, or \ 125.6637061 \ cm}}[/tex]

Step-by-step explanation:

Circumference can be found by multiplying the diameter of the circle by pi.

[tex]c= \pi d[/tex]

We are given the radius, which is 20 centimeters. We need the diameter, which is twice the radius.

[tex]d= 2r[/tex]

[tex]d= 2(20 \ cm)[/tex]

[tex]d= 40 \ cm[/tex]

Substitute the diameter into the formula. There are many ways to calculate circumference, so I included a few options.

1. In Terms of Pi

If we solve in terms of pi, we leave π in the answer.

[tex]c=\pi ( 40 \ cm)[/tex]

[tex]c= 40 \pi \ cm[/tex]

2. Using 3.14 as Pi

[tex]c=\pi ( 40 \ cm)[/tex]

Substitute 3.14 in for pi.

[tex]c= (3.14)(40 \ cm)[/tex]

[tex]c=125.6 \ cm[/tex]

3. Using 3.14159 as PI

[tex]c=\pi ( 40 \ cm)[/tex]

Use the pi button on a calculator.

[tex]c= 125.6637061 \ cm[/tex]

The circumference of the light fixture is 40π, 125.6 cm, or 125.6637061 cm

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Irene​'s car had 6.2 gallons in the 15​-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost ​$3.50 per gallon. How much did Irene spend on​ gas?

Answers

Answer:

She spend $21,70 on gas

Step-by-step explanation:

6.350=2100

$21,00 for 6 gallons

350:10=35

0,35

035.2=070

0,70

2100+70=2170


A circle is cut in half and removed. What is the approximate area (shaded region) of the remaining portion of the circle in square feet? There is a picture of a circle with a line through the middle showing 12 feet.
12 feet ( A=pie(3.14)r^2)
Options are: A. 60 ft2 B. 120 ft2 C. 225 ft2 D. 450 ft2

Answers

Answer:

Step-by-step explanation:

area of a whole circle is pi [tex]r^{2}[/tex]

diameter is 2*r

1/2 * pi * [tex]6^{2}[/tex]   will find the area of 1/2 of the circle that has a diameter of 12'

56.54866 '

so approx  60 ft

PLEASE HELP !!!!! WILL GIVE POINTS !!!!! (√a)=k√a where k=a^n. Find the value of n.

Answers

Answer:

im here for the points

Step-by-step explanation:

im here for the points

plz hellp me plzzzzzzzzzz​

Answers

Answer:

3n+6

Step-by-step explanation:

Can somebody help me please.

Answers

Answer:

The correct answer is the last one: 8 x 16 = ?

Step-by-step explanation:

hope this helps. pls mark this as brainiest if im correct! Thx have a great day... :)

16/8 = 2, 16-8 = 8, 8+16 = 24, 8x16 = 128

What is 5 -90 as a decimal

Answers

-95.00 your answer your welcome

Answer:

-0.85

Step-by-step explanation:

First you subtract 5-90

the answer is -85

then convert -85 to a decimal

the answer is -0.85

can u pls help me with this question ​

Answers

Answer:

c

Step-by-step explanation:

divide 1/5,280 and then multiply that by 6,600

Answer:

the answer is c

Step-by-step explanation:

multiply 6,600 by 1 and that will give you 6,600 again

after that you divide 6,600 and 5,280 that will get you 1.25

if you think I'm wrong just do it on the calculator it will give you 1.25

have a nice day!!

Please help!

What the values of the expression?

A. 3
B. 12
C. 27
D.81

Answers

Answer:

D. 81

Step-by-step explanation:

I am in the same class as you, I took the quiz and the answer was 81

i think it’s 12 but correct me if i’m wrong

4+4=?

help I don't know​

Answers

Answer:

The answer is 8.

Step-by-step explanation:

thank you for the points :)

Write an algebraic expression for the phrase 6 times Z

Answers

Answer:

6z

Step-by-step explanation:

The answer would be 6z = y

PLEASE HELP WILL MARK BRAINLEIST

Answers

Answer:

I belive it's Y = 3/2x - 1

please help !! A.S.A.P

Answers

Answer:

its a black image

Step-by-step explanation:

Answer:

what is this your picture is blank and nothing in the text

John has $40. He will use some of the money to buy books, and he wants to have at least $10 left to put in his savings account. Each book costs $6. a. Write an inequality to represent this story, using b to represent the number of books John buys. b. Solve the inequality, showing each step of your work. c. In complete sentences, explain what the solution means in the context of the story.

Answers

Answer:

3231

Step-by-step explanation:

The answer is in the 3,000 area i messed up to get the exact amount

Hello! :)
Please help me solve this + explain your answer :)

I will indeed give you Brainlst <3

Answers

Answer:

D. (-2, 6)

Step-by-step explanation:

First, isolate a variable in one of the equations (i.e y = or x =)

The first equation already has isolated x.

x = y - 8 or y - 8 = x

5x + y = -4

Substitute the isolated variable into the second equation.

5(y-8) + y = -4

There is now only one variable, y, in the equation. Now you can solve for y.

First, use the distributive property to get the equation

5y - 40 + y = -4

Then, add 40 to both sides.

5y + y = 36

Add like-terms.

6y = 36

Divide.

36 / 6 = 6

So, y = 6.

Now that we have one coordinate, y = 6, you can substitute for y in the first equation.

x = 6 - 8

Subtract.

x = -2

Your coordinates are now x = -2 and y = 6, or (-2, 6).

Ryan had some candy to give to his five children. He first took eight pieces for
himself and then evenly divided the rest among his children. Each child received four pieces. With how many pieces did he
start?

Answers

Answer:

28 pieces

Step-by-step explanation:

5 kids x 4 pieces = 20 pieces

20 + dad's 8 pieces = 28 pieces of candy

He has 5 children and each get for so = 20 + his 8 which equals 28

Simplify the expression 8+4b+3b+6

Answers

Answer:

14+7b

Step-by-step explanation:

8+6=14

4b+3b=7b

Answer:

14 +7b

Step-by-step explanation:

Combine like terms. Like terms have same variables

8 + 4b + 3b + 6 = 8 + 6 + 4b + 3b

                           = 14 + 7b

There is 7/8 of the pretzel bag left. If one serving is 1/4 of the bag. How many servings are left? Use the model to answer the question.

Answers

Answer:

5/8

Step-by-step explanation:

What % of 25 is 15. Please help me

Answers

Answer:

15 is 60% (percent) of 25.

Step-by-step explanation:

can someone give me answers pls asap

Answers

Answer:

answers are:

1) 1.75

2) 1.25

please help me i need help i'll help you if you help me !
i will mark you as brill

Answers

Answer:

See Explanation

Step-by-step explanation:

Required

Write three equivalent ratios

To solve these questions, we do the following:

Whatever is being applied to a part of the ratio must be done on the other part

Solving (9):

[tex]Ratio = \frac{2}{7}[/tex]

Multiply through by 2

[tex]Ratio = \frac{2*2}{7*2} = \frac{4}{14}[/tex]

Multiply through by 3

[tex]Ratio = \frac{2*3}{7*3} = \frac{6}{21}[/tex]

Multiply through by 5

[tex]Ratio = \frac{2*5}{7*5} = \frac{10}{35}[/tex]

Hence, the equivalents are: [tex]\frac{4}{14}, \frac{6}{21}, \frac{10}{35}[/tex]

Solving (10):

Ratio = 1.5 to 3.5

Multiply by 2

[tex]Ratio = 1.5 * 2\ to\ 3.5 * 2[/tex]

[tex]Ratio = 3\ to\ 7[/tex]

Multiply by 3

[tex]Ratio = 1.5 * 3\ to\ 3.5 * 3[/tex]

[tex]Ratio = 4.5\ to\ 10.5[/tex]

Multiply by 4

[tex]Ratio = 1.5 * 4\ to\ 3.5 * 4[/tex]

[tex]Ratio = 6\ to\ 14[/tex]

Hence, the equivalents are:  3 to 7, 4.5 to 10.5 and 6 to 14

Solving (11):

Ratio = 6.25 to 1.25

Divide by 5

[tex]Ratio = 6.25/5\ to\ 1.25/5[/tex]

[tex]Ratio = 1.25\ to\ 0.25[/tex]

Multiply by 2

[tex]Ratio = 6.25*2\ to\ 1.25*2[/tex]

[tex]Ratio = 12.5\ to\ 2.5[/tex]

Multiply by 4

[tex]Ratio = 6.25*4\ to\ 1.25*4[/tex]

[tex]Ratio = 25\ to\ 5[/tex]

Hence, the equivalents are:  1.25 to 0.25, 12.5 to 2.5 and 25 to 5

Solving (12):

[tex]Ratio = 3 : 3\frac{1}{2}[/tex]

Multiply by 2

[tex]Ratio = 3 *2: 3\frac{1}{2}*2[/tex]

[tex]Ratio = 6: 7[/tex]

Multiply by 4

[tex]Ratio = 3 *4: 3\frac{1}{2}*4[/tex]

[tex]Ratio = 12: 14[/tex]

Multiply by 6

[tex]Ratio = 3 *6: 3\frac{1}{2}*6[/tex]

[tex]Ratio = 18: 21[/tex]

Hence, the equivalents are: 6:7, 12:14 and 18:21

Solving (13)

[tex]Ratio = 1\frac{2}{3} : \frac{5}{4}[/tex]

Convert mixed fraction to improper fraction

[tex]Ratio = \frac{5}{3} : \frac{5}{4}[/tex]

Multiply by 2

[tex]Ratio = \frac{5}{3}*2 : \frac{5}{4}*2[/tex]

[tex]Ratio = \frac{10}{3} : \frac{5}{2}[/tex]

Multiply by 3

[tex]Ratio = \frac{5}{3}*3 : \frac{5}{4}*3[/tex]

[tex]Ratio = 5 : \frac{15}{4}[/tex]

Multiply by 12

[tex]Ratio = \frac{5}{3}*12 : \frac{5}{4}*12[/tex]

[tex]Ratio = 20 : 15[/tex]

Hence, the equivalents are: 10/3:5/2, 5 : 15/4, and 20:15

Other Questions
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