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14.05.2022

2 to the power minus 6 as a fraction

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09.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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$2 to the power minus 6 as a fraction, №18010411, 14.05.2022 21:21$

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$2 to the power minus 6 as a fraction, №18010411, 14.05.2022 21:21$

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Mathematics

2 to the power minus 6 as a fraction

Step-by-step answer

P Answered by Specialist

$\frac{1}{64}$

Step-by-step explanation:

$2^{-6}$

$= \frac{1}{2^{6}}$

$= \frac{1}{64}$

Mathematics

What is the sum of the first seven terms of the geometric series 2 − 8 + 32 − . . ? hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio. s7 = 6,554 s7 = −8,192 s7 = 8,192 s7 = 10,922

Step-by-step answer

P Answered by PhD

S_7=6554

Step-by-step explanation:

The given series is 2-8+32-...

The first term of the sequence is

a_1=2

There is a common ratio of

r=-4

The sum of the first n terms of a geometric sequence is given by the formula;

$S_n=\frac{a_1(1-r^n)}{1-r}$

We want to find the first seven terms so n=7

We substitute the given values into the formula to obtain;

$S_7=\frac{2(1-(-4)^7)}{1--4}$

$S_7=\frac{2(1--16384)}{1--4}$

$S_7=\frac{2(16385)}{5}$

S_7=2(3277)

S_7=6554

The correct answer is A

Mathematics

How many terms are there in a geometric series if the first term is 2, the common ratio is 4, and the sum of the series is 2,730? hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio. n = 3 n = 4 n = 5 n = 6

Step-by-step answer

P Answered by PhD

n = 6

Step-by-step explanation:

Givens

r = 4

a = 2

Sum = 2730

Equation

Sum = a(1 - r^n)/(1 - r)

Solution

2730 = 2 (1 - 4^n) / (1 - 4) Reduce the denominator

2730 = 2(1 - 4^n)/-3 Multiply both sides by -3

2730*-3 = 2(1 - 4^n) Simplify the left

-8190 = 2(1 - 4^n) Divide by 2

-8190/2 = 1 - 4^n Simplify

-4095 = 1 - 4^n Subtract 1 from both sides.

-4096 = - 4^n Divide by - 1

4096 = 4^n This looks like n is fairly large. You could use logs. Try n = 6.

4^6 does equal 4096 So your answer is 6.

Let's try it with logs. Ignore this if you don't know how to do this.

log(4096) = log(4)^n

log(4096) = n*log(4) Divide by log 4

log(4096)/log(4) = n

3.6124 / 0.6021 = n

n = 6

The hint is very helpful. Make sure you can follow it through

Mathematics

Step-by-step answer

P Answered by PhD

S_7=6554

Step-by-step explanation:

The given series is 2-8+32-...

The first term of the sequence is

a_1=2

There is a common ratio of

r=-4

The sum of the first n terms of a geometric sequence is given by the formula;

$S_n=\frac{a_1(1-r^n)}{1-r}$

We want to find the first seven terms so n=7

We substitute the given values into the formula to obtain;

$S_7=\frac{2(1-(-4)^7)}{1--4}$

$S_7=\frac{2(1--16384)}{1--4}$

$S_7=\frac{2(16385)}{5}$

S_7=2(3277)

S_7=6554

The correct answer is A

Mathematics

Step-by-step answer

P Answered by PhD

n = 6

Step-by-step explanation:

Givens

r = 4

a = 2

Sum = 2730

Equation

Sum = a(1 - r^n)/(1 - r)

Solution

2730 = 2 (1 - 4^n) / (1 - 4) Reduce the denominator

2730 = 2(1 - 4^n)/-3 Multiply both sides by -3

2730*-3 = 2(1 - 4^n) Simplify the left

-8190 = 2(1 - 4^n) Divide by 2

-8190/2 = 1 - 4^n Simplify

-4095 = 1 - 4^n Subtract 1 from both sides.

-4096 = - 4^n Divide by - 1

4096 = 4^n This looks like n is fairly large. You could use logs. Try n = 6.

4^6 does equal 4096 So your answer is 6.

Let's try it with logs. Ignore this if you don't know how to do this.

log(4096) = log(4)^n

log(4096) = n*log(4) Divide by log 4

log(4096)/log(4) = n

3.6124 / 0.6021 = n

n = 6

The hint is very helpful. Make sure you can follow it through

Mathematics

Quickly! i suck at the word with the definition: 1. devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed 2. an expression that consists of numbers, operations, and sometimes grouping symbol. 3. the order in which operations must be computed when more than one operation is involve. 4. a number representing how many times the base number should be multiplied by itself. 5. a symbol that represents a value that can change. 6. a single number or variable,

Step-by-step answer

P Answered by Specialist

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 : Evaluate

14 : Open Sentence

Mathematics

With math vocab will give brainliest1. devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed 2. an expression that consists of numbers, operations, and sometimes grouping symbol. 3. the order in which operations must be computed when more than one operation is involve. 4. a number representing how many times the base number should be multiplied by itself. 5. a symbol that represents a value that can change. 6. a single number or variable, or numbers

Step-by-step answer

P Answered by Specialist

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 :

14 : Open Sentence

Those are the ones I know. I hope this helps

Mathematics

Match the word to the definition. put the number of the definition next to the word to match. operator grouping symbol open sentence inequality coefficient variable expression order of operations evaluate constant equation variable term exponent (power) numerical expression 1. devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed 2. an expression that consists of numbers, operations, and sometimes grouping symbol. 3. the order in which operations

Step-by-step answer

P Answered by Specialist

The number is the def.

Grouping symbol = 1

Inequality = 12

Variable expression = 13

Order of operations = 3

Evaluate = 10

Constant = 8

Equation = 11

Variable = 5

Term = 6

Mathematics

Step-by-step answer

P Answered by Specialist

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 : Evaluate

14 : Open Sentence

Mathematics

Step-by-step answer

P Answered by Specialist

The number is the def.

Grouping symbol = 1

Inequality = 12

Variable expression = 13

Order of operations = 3

Evaluate = 10

Constant = 8

Equation = 11

Variable = 5

Term = 6

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2 to the power minus 6 as a fraction

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