a and b are positive integers and a-b=2. Evaluate the following:
9^1/2b/3^a

A And B Are Positive Integers And A-b=2. Evaluate The Following:9^1/2b/3^a

Answers

Answer 1

Answer:

[tex] \frac{1}{ 9 }[/tex]

Step-by-step explanation:

[tex] \huge \frac{ {9}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ {( {3}^{2} )}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ { {3}}^{2 \times \frac{1}{2}b } }{ {3}^{a} } \\ \\ \huge = \frac{ {3}^{b} }{ {3}^{a} } \\ \\ \huge = \frac{1}{ {3}^{a - b} } \\ \\ \huge= \frac{1}{ {3}^{2} } \\ ( \because \: a - b = 2)\\ \\ \huge = \frac{1}{ 9 }[/tex]

Answer 2

The evaluation of the expression 9^((1/2)b)/3^a is 1/9

What are some basic properties of exponentiation?

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]

Now, for this case, we are given that:

a - b = 2

The expression is:

[tex]\dfrac{9^\dfrac{1}{2}b}{3^a}[/tex]

Since we know that [tex]3^2 = 9[/tex], thus:

[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} = \dfrac{(3^2)^{\frac{1}{2}b}}{3^a} = \dfrac{3^{2 \times 1/2 \times b}}{3^a} = \dfrac{3^b}{3^a} = \dfrac{1}{3^{a-b}}[/tex]

Since a-b = 2, therefore, we get:
[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} =\dfrac{1}{3^{a-b}} = \dfrac{1}{3^2}} = \dfrac{1}{9}[/tex]

Thus, the evaluation of the expression 9^((1/2)b)/3^a is 1/9

Learn more about exponentiation here:

https://brainly.com/question/15722035


Related Questions

Create and solve a 2 step equation where x = -3

Answers

Answer:

Equation:

x + 2 = -1

x = -1 - 2

x = 3

One number is 5 more than another number. Three times the greater plus twice the lesser is 30. Determine the numbers.

Answers

Answer:

.

Step-by-step explanation:

Answer:

Step-by-step explanation:

One number is 5 more than another number. Three times the first plus twice the second is 30.Find the numbers.

x = first number

y = second number

x=y+5

3x +2y = 30

lets substitute x=y+5 in the second equation for x;

3(y+5) + 2y =30

3y + 15 + 2y = 30

5y + 15 =30

5y = 30 -15

5y = 15

y = 3

Now that we have y lets plug that answer into either equation for y;

x = 3 + 5

x = 8

:) if I’m wrong I’m very sorry.

Find the value of x then find the angle measures of the polygon

Answers

Answer:

X=135⁰

Step-by-step explanation:

The sum of angles= 540

Angles are x⁰ x,⁰(x-45⁰),(x-45)⁰

x+x+x+x-45+x-45+x-45=540

5x-135=540   simplify

5x=540+135   Add 135 to both sides

[tex]\frac{5x}{5} =\frac{675}{5}[/tex]

divide both sides by 5

X=135⁰

hope it helps....

Help me, I will give brainliest to best answer. No work needs to be explained.

Write three hundreths as a decimal.

Use digits to write each decimal number:
a. one hundred two and three tenths
b. one hundred twenty-five ten-thousandths
c. three hundred and seventy-five thousandths

Answers

Answer:

3.00 I think or 30.0 I really don't know but that's what I think

2. Eli has 600 cubes that are 1 cubic inch. Select the smallest length a cube- shaped box can have while being able to hold the 600 cubes. A 7 in. B 8 in. C 9 in. D 10 in.

Answers

Answer:

9 in

Step-by-step explanation:

We need to find x in x^3 > 600

For x=8, 8^3 = 512 < 600 (Too Small)

For x=9, 9^3 = 729 > 600 (Just right)

For x=10, 10^3 = 1000 > 600 (Too big)

Therefore, the smallest length of the cube-shaped box is 9 in.

I need help, please anyone!

Answers

1.45 is the answer! brainliest

Please help... 12 points please thank you!

Answers

Number of dollars I think
Sorry if I’m wrong

Joey and her sister are helping remodel their parent's house.

They plan to carpet the bedroom which is 14 feet by 16 feet.

The carpet is priced at $1.90 per square foot.

How much can they expect to pay for the new carpet?

Answers

Answer:

They will have to pay $425.60

Step-by-step explanation:

14*16 equals 224 feet

224 feet times $1.90 equals $425.60

y = -3/2x -2 y = -1/4 + 3

Answers

Answer:

umm. what am I supposed to find

Step-by-step explanation:

I need to know what to fi d in order to get the answer for you it would make it easier if you did that now so yeah

Can you guys plz help me!?
Thanks!!

Answers

X=10 as the 2 angles are the same

-5x=10 plz no links thanks

Answers

Answer:

2

Step-by-step explanation:

2x5=10

Answer:

-5x=10

x= 10/(-5)

x = -2 (sign in the denomiantor comes to numerator)

What is the length of JK¯¯¯¯¯, to the nearest tenth of a millimeter? 4.5 mm 5.6 mm 8.3 mm 19.9 mm A horizontally-aligned scalene triangle J K L. Side J L is labeled as 3 millimeters. Side L K is labeled as 5 millimeters. Angle L is labeled as 62 degrees.

Answers

Answer:

5 = side a

3 = side c

angle B = 62 degrees

JK is side b

Use the Law of Cosines to find the length of side b.

b^2 = a^2 + c^2 − 2ac cos(B)

b^2 = (5^2 + 3^2) − ( 2 x 5 x 3) cos(62°)

b^2 = (25 + 9) − 30 x 0.469

b^2 = 34 - 30 x 0.469

b^2 = 34 - 14.084

b^2 = 19.916

b = √19.916

b = 4.463

Rounded to the nearest tenth is 4.5 mm.

Hope this helps!

Step-by-step explanation:

Answer:

4.5 mm

Step-by-step explanation:

There are 120 pieces of candy in a bag. Fill in the table below to determine the number of pieces of each color

Answers

Answer:

Blue = 30

Green = 24

Red = 54

Orange = 12

Step-by-step explanation:

hahahshahhahahahahahauehfudbrog f ghg

Need help once again!!!

Answers

Answer:

the answer to this question is seven

16. Solve for x. x = __________

Answers

Answer:

20

Step-by-step explanation:

Urgent!! Math help!!! Pls answer them all or the ones you know! I’ll make you brain-list!

Answers

Answer:

1) mEF is 38°

2) mDE is 52°

3) c. 6.28

4) b. 20.94

Step-by-step explanation:

1) mEF is corresponding to mHG

2) mDE + mEF = 90, so 90-38=52

3) L=r·∅    so L=3·120 (in radians)

4) Couldn't see Q, but based on the right angle we can assume the inside angle for mQPT is 119°

Mrs Chen buys 3 identical boxes of chocolates from a super market .
She uses a $50 note to pay for them and gets $8 change. How much does
each box of chocolates cost?

Answers

Answer:

50 - 8 = 42

divide 42 by 3!

5.25

Solve the system using the substitution method. -5x – 8y = 17 x = 3.5y – 8.5 NO LINKS PLEASE HELP LINKS = REPORT

Answers

Answer:

x=-5 , y=1

Step-by-step explanation:

-5x-8y=17

x=3.5y-8.5

-5(3.5y-8.5)-8y=17

-17.5y+42.5-8y=17

-25.5y+42.5=17

-25.5y=-25.5

y=1

x=3.5(1)-8.5

x=-5

What is the slope-intercept equation for the line below?
5
(54)
(0, 2)
- A. y = 2 x + 2
D. -- +2

Answers

It would be at 35 when you work all then problems together

Help me please I will give Brainliest!

Answers

Answer:

n = 4.5

Step-by-step explanation:

I think it is 4.5 because n is 3 units ahead of 1.5 on the number line:

1.5+3=4.5

can you please help me? as much as you can is greatly appreciated <333 pt 2

Answers

Answer: m3 for the first one

Step-by-step explanation:de

This could take a while, so I'll simply put the answer with the theorem I used to figure it out with.

1) 45° - minor arc; Central Angles/Arcs Theorem

2) 180° - semi circle; Diameter Theorem? (Whichever theorem states that the diameter separates a circle into two 180° semi circles)

3) 75° - minor arc; Angle Addition Postulate

4) 105° - minor arc; Angle Addition Postulate

5) 225° - major arc; Angle Addition Postulate

6) 45° - minor arc; Vertical Angles Theorem

7) 135° - minor arc; Angle Addition Postulate

8) 240° - major arc; Angle Addition Postulate

9) 315° - major arc; Angle Subtraction Postulate, i think? lol.

10) 180° - semi circle; Diameter Theorem or whatever it's called lol.

Additionally, I determined whether or not an angle was a major arc, minor arc, or semi circle with the knowledge that:

minor arc - less than 180 degreesmajor arc - more than 180 degreessemi circle - is 180 degrees.

Have a nice day, fam. Spread The Love. lol I'm tired after typing all this out :P

Rewrite the decimals as fractions 3.34

Answers

167/50 is a fraction i got

can you please help me? as much as you can is greatly appreciated <333 pt 1

Answers

Answer:

11) 80°

12) 80°

13) 80°

14) 40°

15) 60°

16) 120°

17) 180°

18) 100°

19) 120°

20) 280°

Step-by-step explanation:

This will take awhile, so I will just give you the theorems I used to determine my answer.

11) Supplementary angles theorem

12) Central Angles/Arcs Theorem

13) Vertical Angles Theorem

14) Central Angles/Arcs Theorem

15) Vertical Angles Theorem (The vertical angle minus 40 would equal 60)

16) Supplementary Angles Theorem (Supplementary to 100 degrees)

17) Central Angles/Arc Theorem

18) Vertical Angles & Central Angles/Arc Theorem

19) Angle Addition Postulate, somewhat

20) Angle Addition Postulate

Have a nice day, fam. This problem really worked my brain. Spread The Love.

what is the answer of 2m^2 * 2m^3

Answers

Answer:

4m^5

Step-by-step explanation:

Answer:

4m^5

Step-by-step explanation:

PLS HELP QUICK!!

The volume V of a cylinder with radius r and height h is given by the formula V = (pi)r^2h. Solve the formula for r. Then find the radius of a cylinder with a height of 15 centimeters and a volume of 750cubic centimeters. Round to the nearest hundredth.

Answers

Answer:

4

Step-by-step explanation:

750=3.14 × r^2 ×15 you divide 750 by 3.14 then by 15, then you take the square root

Describe a real world situation where you might use the Pythagorean Theorem. Help due today :))

Answers

Answer: When carpenters want to construct a guaranteed right angle, they can make a triangle with sides 3, 4, and 5 (units). By the Pythagorean Theorem, a triangle made with these side lengths is always a right triangle, because
3^2
+
4^2
=
5^2


Explanation: hope this helps

What is 5x6 equal too?

Answers

Answer:

30

Step-by-step explanation:

6+6+6+6+6 or 5+5+5+5+5+5

Answer:

30

Step-by-step explanation:

cause you can do it mentally or you can do 5+5+5+5+5+5, cause its 5 six times. Or 6 five times. 6+6+6+6+6

Rewrite this number in scientific notation.
57,000,000,000,000

Answers

Answer:

57.0 * 10^12

Step-by-step explanation:

Answer:

5.7 x 10^13

Step-by-step explanation:

trust me

Mary spent a total of $322.53 for a party. She spent $200.97 on food, plus an additional $30.39 for each hour of the party. How long
was the party?

Answers

Answer:

4 hours

Step-by-step explanation:

y = total cost

x = per hour

Equation:

y = 200.97 + 30.39x

322.53 = 200.97 + 30.39x

322.53 - 200.97 = 30.39x

121.56 = 30.39x

x = 4

322.53 - 200.97 = 121.56

121.56 is the money she has left over after buying food so
121.56/30.39=4 hours

What are two numbers that when multiplied equal -30 and when added together equal 1?

Answers

Answer:

6 and -5

Step-by-step explanation:

6 times -5 = -30

6 + (-5) = 1

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