Question

Simplify (2^-8)^-2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify (2^-8)^-2, we can use the property of exponents that states: (a^m)^n = a^(m*n).

So (2^-8)^-2 = 2^(-8*-2) = 2^16.

Answer 2

Exponential form

Answer 3

[AI-generated answer — Bot GPT 3.5]

The exponential form of 2^16 is 65,536.

Answer 4

Simplify and write (2^-8)^-2 in exponential form

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify and write (2^-8)^-2 in exponential form, first, let's simplify the expression inside the parentheses:

(2^-8)^-2 = (1/2^8)^-2 = (1/256)^-2

Next, we can rewrite 1/256 as a power of 2 using negative exponents:

(1/256)^-2 = (2^-8)^-2

Now, we can write the expression in exponential form as:

(2^-8)^-2 = 2^16

Answer 6

Simplify 2^16

Answer 7

[AI-generated answer — Bot GPT 3.5]

2^16 simplifies to 65,536.

Answer 8

Simplify 65,536

Answer 9

[AI-generated answer — Bot GPT 3.5]

65,536 is already simplified, as it is the numerical representation of 2^16.

Answer 10

Simplify 2^-8×^-2 in exponential form

Answer 11

[AI-generated answer — Bot GPT 3.5]

To simplify 2^-8×^-2 in exponential form, we can use the property of exponents that states: a^(-n) = 1/(a^n).

So, 2^-8 ×^-2 = 1/(2^8 × 2^2) = 1/(2^8 × 4) = 1/(256 × 4) = 1/1024.

Answer 12

@bot

I want you to simplify 2^-8×^-2

EXPONENTIAL FORM

Your answers you have provided are all incorrect

Please provide me the right answer!!

Hint: The answer is not 1, 1024, 1/1024, 2^16, or 65,536

Answer 13

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's simplify 2^-8 × ^-2 using exponential form.

To simplify this expression, we can use the rule that states: a^(-n) = 1/(a^n).

So, 2^-8 × ^-2 can be rewritten as 1/(2^8) × 1/(2^2).

Using the rules of exponents, we can simplify this to 1/((2^8) × 2^2) = 1/(2^8 × 2^2) = 1/2^(8+2).

Combining the exponents, we get 1/2^10.

Therefore, the simplified form, written in exponential form, is 2^(-10).

Answer 14

@bot

That is also not the correct answer

Answer 15

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's simplify 2^-8 ×^-2 using exponential form.

To simplify this expression, we can combine the exponents. The rule for multiplying numbers with negative exponents is to add the exponents.

So, 2^-8 ×^-2 can be simplified as 2^(-8 + (-2)) = 2^(-8 - 2) = 2^-10.

Therefore, the simplified form, written in exponential form, is 2^-10.

Answer 16

Solve (z^5)^?=z^60

Answer 17

[AI-generated answer — Bot GPT 3.5]

To solve the equation (z^5)^x = z^60, we can equate the exponents:

5x = 60

Dividing both sides by 5, we get:

x = 12

Therefore, the value of x that satisfies the equation is x = 12.

Answer 18

Solve (z^3)^?=z^-15

Answer 19

[AI-generated answer — Bot GPT 3.5]

To solve the equation (z^3)^x = z^-15, we can equate the exponents:

3x = -15

Dividing both sides by 3, we get:

x = -5

Therefore, the value of x that satisfies the equation is x = -5.

Answer 20

(z^-5)^-9

Answer 21

[AI-generated answer — Bot GPT 3.5]

To simplify (z^-5)^-9, we can use the rule of exponents which states that (a^m)^n = a^(mn).

Applying this rule, we have:

(z^-5)^-9 = z^(-5 * -9)

Multiplying the exponents, we get:

z^(45)

Therefore, (z^-5)^-9 simplifies to z^45.

Answer 22

Solve (y^8)^?=y^16

Answer 23

[AI-generated answer — Bot GPT 3.5]

To solve the equation (y^8)^x = y^16, we can equate the exponents:

8x = 16

Dividing both sides by 8, we get:

x = 2

Thus, the value of x that satisfies the equation is x = 2.

Answer 24

Solve (x^?)^2=x^-36

Answer 25

[AI-generated answer — Bot GPT 3.5]

To solve the equation (x^?)^2 = x^-36, we can equate the exponents:

2 * ? = -36

Dividing both sides by 2, we get:

? = -36/2

Simplifying further, we have:

? = -18

Therefore, the value of ? that satisfies the equation is ? = -18.

Answer 26

Solve (x^?)^2=x^84

Answer 27

[AI-generated answer — Bot GPT 3.5]

To solve the equation (x^?)^2 = x^84, we can equate the exponents:

2 * ? = 84

Dividing both sides by 2, we get:

? = 84/2

Simplifying further, we have:

? = 42

Therefore, the value of ? that satisfies the equation is ? = 42.

Answer 28

Solve (x^?)^6=x^84

Answer 29

[AI-generated answer — Bot GPT 3.5]

To solve the equation (x^?)^6 = x^84, we can equate the exponents:

6 * ? = 84

Dividing both sides by 6, we get:

? = 84/6

Simplifying further, we have:

? = 14

Therefore, the value of ? that satisfies the equation is ? = 14.

Answer 30

Solve (x^?)^7=x^63

Answer 31

[AI-generated answer — Bot GPT 3.5]

To solve the equation (x^?)^7 = x^63, we can equate the exponents:

7 * ? = 63

Dividing both sides by 7, we get:

? = 63/7

Simplifying further, we have:

? = 9

Therefore, the value of ? that satisfies the equation is ? = 9.

Answer 32

Simplify (y^8)^7

Answer 33

[AI-generated answer — Bot GPT 3.5]

To simplify (y^8)^7, we can use the property of exponents that states (a^m)^n = a^(m*n).

Applying this property, we have:

(y^8)^7 = y^(8*7) = y^56

Therefore, (y^8)^7 simplifies to y^56.

Answer 34

Simplify (3^9)^3

Answer 35

[AI-generated answer — Bot GPT 3.5]

To simplify (3^9)^3, we can apply the property of exponents that states (a^m)^n = a^(m * n).

Applying this property, we have:

(3^9)^3 = 3^(9 * 3) = 3^27

Therefore, (3^9)^3 simplifies to 3^27.

Answer 36

Simplify (6^2)^4 using the power rule of exponents

Answer 37

[AI-generated answer — Bot GPT 3.5]

To simplify (6^2)^4 using the power rule of exponents, we need to multiply the exponents:

(6^2)^4 = 6^(2 * 4) = 6^8

Therefore, (6^2)^4 simplifies to 6^8.

Answer 38

Simplify (73^4)^5 using the power rule of exponents

Answer 39

[AI-generated answer — Bot GPT 3.5]

To simplify (73^4)^5 using the power rule of exponents, we multiply the exponents:

(73^4)^5 = 73^(4 * 5) = 73^20

Therefore, (73^4)^5 simplifies to 73^20.

Answer 40

Use the power rule of exponents to simplify (78^8)^6

Answer 41

[AI-generated answer — Bot GPT 3.5]

To simplify (78^8)^6 using the power rule of exponents, we multiply the exponents:

(78^8)^6 = 78^(8 * 6) = 78^48

Therefore, (78^8)^6 simplifies to 78^48.

Answer 42

Use the power rule of exponents to simplify (12×12×12)×(12×12×12)

Answer 43

[AI-generated answer — Bot GPT 3.5]

To simplify (12 × 12 × 12) × (12 × 12 × 12) using the power rule of exponents, we can rewrite it as (12^3) × (12^3).

Using the power rule, we add the exponents when multiplying two numbers with the same base:

(12^3) × (12^3) = 12^(3 + 3) = 12^6.

Therefore, (12 × 12 × 12) × (12 × 12 × 12) simplifies to 12^6.

Answer 44

What exponent would make (16^x)^6 equal to (16^18)

Answer 45

[AI-generated answer — Bot GPT 3.5]

To find the exponent that would make (16^x)^6 equal to (16^18), we can equate the exponents:

6x = 18

Dividing both sides by 6, we get:

x = 3

Therefore, the exponent that makes (16^x)^6 equal to (16^18) is x = 3.

Answer 46

Which expression is correctly developed to use the power rule of exponents

(7^4)^8

(-5)^0

12^9

(7^8)×(7^10)

Answer 47

[AI-generated answer — Bot GPT 3.5]

The expression that is correctly developed to use the power rule of exponents is:

(7^4)^8.

According to the power rule, we can multiply the exponents:

(7^4)^8 = 7^(4 * 8) = 7^32.

Therefore, the expression (7^4)^8 can be simplified using the power rule of exponents.

Answer 48

Which of the following correctly used the power rule of exponents in the expression (10^9)^7

10^2

90^7

10^63

10^16

Answer 49

[AI-generated answer — Bot GPT 3.5]

The expression that correctly uses the power rule of exponents for (10^9)^7 is:

10^63.

According to the power rule, we multiply the exponents:

(10^9)^7 = 10^(9 * 7) = 10^63.

Therefore, the expression 10^63 correctly uses the power rule of exponents for (10^9)^7.

Answer 50

If the expression 4^10 was simplified using the power rule of exponents, what is an equivalent expanded expression?

(4^12)^2

(4^5)^2

4×4×4×4×4×4×4

(4^2)^8

Answer 51

[AI-generated answer — Bot GPT 3.5]

If the expression 4^10 is simplified using the power rule of exponents, an equivalent expanded expression would be:

4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

This expression represents the repeated multiplication of the base 4, 10 times, as stated by the exponent 10 in the original expression.

Answer 52

That is wrong

Answer 53

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. If the expression 4^10 is simplified using the power rule of exponents, the equivalent expanded expression would be:

4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

Alternatively, we can write it as 4^1 × 4^1 × 4^1 × 4^1 × 4^1 × 4^1 × 4^1 × 4^1 × 4^1 × 4^1, which is equal to 4^(1+1+1+1+1+1+1+1+1+1) = 4^10.

Please let me know if you have any further questions or need additional clarification.