I need all of these answers with work shown and/or explained, please help..

1. -(5)^-1

Answer:-1/5

3. -1/y^-4

Answer: -y^4

4. 5 ^ 4 x 5^7

Answer: 5^11

7. (5t ^ 3)^-4

Answer: 1/625t^12

12. What is the order of 4 x 10^-7, 7 x 10^-9, 1 x 10^4, 2 x 10^4

Answer: 7 x 10^-9, 4 x 10^-7, 1 x 10^4, 2 x 10^4

13. Find the simplified form of the expression. Give your answer in scientific notation
(8 x 10^4)(9 x 10^-8)

Answer: 7.2 x 10^-3

14. Astronomers measure long distances in light-years. One light year is the distance that light can travel in one year, or approcimately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light-years from Earth. in scienctific notation, approximately how many miles is it?

Answer: 5.76 x 10^14 miles

15. A dinosaur fossil is 91,910,000 years old. How canyou express this age in scientific notation with the highest level of precision?

Answer: 9.191x10^7

16. Radio signals travel at a rate of 3 x 10^8 meters per second. How many seconds would it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of 3.6 x 10^7 meters? (Hint: Time is distance divided by rate.)

Answer: 1.2 x 10^-1

18. Does the rule y=6x^7 represent an exponential function?

Answer: no

i like chickken

1. -(5)^-1 = 1/-(5) = -1/5.

3. Similar to #1.

4. a^4 * a^7 = a^11
5^4 * 5^7 = 5^11.

7. (5t^3)^-4 =
1/(5t^3)^4 =
1/(5^4t^12) = 1/(625t^12).

12. 4*10^-7 = 400*10^-9 and is much larger than 7*10^-9;
therefore, it is the smallest in the order.

13. (8*10^4) (9*10^-8) = 72*10^-4 = 7.2*10^-3.

14. d = 5.88*10^12miles/light-year * 9.8*10^1light-years = 5.76*10^14 miles.

16. V*T = 3.6*10^7
3*10^8T = 3.6*10^7
T =

1. -(5)^-1

Explanation:
To solve this, we start by evaluating the exponent first. (-1) means we need to take the reciprocal, so we have 1/5. Since we have a negative sign in front, the final answer is -1/5.

3. -1/y^-4

Explanation:
Similar to the previous problem, we start by evaluating the exponent. (-4) means we need to take the reciprocal, so we have 1/y^4. Also, since we have a negative sign in front, the final answer is -y^4.

4. 5^4 x 5^7

Explanation:
When multiplying numbers with the same base, we add the exponents. So, 5^4 x 5^7 = 5^(4+7) = 5^11.

7. (5t^3)^-4

Explanation:
To solve this, we apply the exponent to both the base and the exponent inside the parentheses. So, (5t^3)^-4 = 5^-4t^-12. Since we have a negative exponent, we take the reciprocal, resulting in 1/5^4t^12 = 1/625t^12.

12. Order: 4 x 10^-7, 7 x 10^-9, 1 x 10^4, 2 x 10^4

Explanation:
To determine the order, we compare the exponents. In increasing order, we have: 7 x 10^-9, 4 x 10^-7, 1 x 10^4, 2 x 10^4.

13. (8 x 10^4)(9 x 10^-8)

Explanation:
To simplify this expression, we multiply the coefficients and add the exponents. (8 x 10^4)(9 x 10^-8) = 72 x 10^-4 = 7.2 x 10^-3.

14. Approximately how many miles is a star that is 9.8 x 10^1 light-years from Earth?

Explanation:
To convert light-years to miles, we multiply the given value by the conversion factor: 5.88 x 10^12 miles. So, 9.8 x 10^1 light-years multiplied by 5.88 x 10^12 miles = 5.76 x 10^14 miles.

15. How can you express the age of a dinosaur fossil, 91,910,000 years old, in scientific notation?

Explanation:
To express this age in scientific notation, we move the decimal point to create a number between 1 and 10. So, 91,910,000 becomes 9.191 x 10^7.

16. How many seconds would it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of 3.6 x 10^7 meters?

Explanation:
Using the formula Time = Distance / Rate, we divide the distance (3.6 x 10^7 meters) by the rate of travel (3 x 10^8 meters per second). So, Time = (3.6 x 10^7) / (3 x 10^8) = 1.2 x 10^-1 seconds.

18. Does the equation y = 6x^7 represent an exponential function?

Explanation:
No, the equation y = 6x^7 does not represent an exponential function. Exponential functions have the form y = ab^x, where b is a constant and x appears in the exponent. In this case, x is raised to the 7th power, but the base is fixed at 6.

To solve these problems and show the work or explanation, let's go through each one step by step:

1. -(5)^-1:
To simplify this expression, you need to evaluate the exponent first. When a negative sign is raised to an exponent, it results in the reciprocal of the base raised to that exponent. So (-1)^-1 is equal to -1/1, which simplifies to -1.

3. -1/y^-4:
In this expression, you have a negative sign followed by 1 divided by y raised to the power of -4. Any number raised to the power of -n is equal to its reciprocal raised to the power of n. So, y^-4 becomes 1/y^4. Therefore, the answer is -1/y^4.

4. 5^4 x 5^7:
To simplify this expression, you need to combine the two expressions with the same base by adding their exponents. So, 5^4 x 5^7 becomes 5^(4+7), which is equal to 5^11.

7. (5t^3)^-4:
In this expression, you have a base of (5t^3) raised to the power of -4. To simplify it, you need to apply the power to both the base and the exponent inside the parentheses. So, (5t^3)^-4 becomes 1/(5^4t^(3*4)), which simplifies to 1/625t^12.

12. Order of 4 x 10^-7, 7 x 10^-9, 1 x 10^4, 2 x 10^4:
To determine the order of these numbers, you compare the exponents of 10. The smaller the exponent, the larger the number. So, the correct order is 7 x 10^-9, 4 x 10^-7, 1 x 10^4, 2 x 10^4.

13. (8 x 10^4)(9 x 10^-8):
To simplify this expression, you multiply the coefficients together and add the exponents of 10. So, (8 x 10^4)(9 x 10^-8) becomes 72 x 10^(4+(-8)), which simplifies to 72 x 10^-4. In scientific notation, this is written as 7.2 x 10^-3.

14. Distance in miles of a star, given in light-years:
To find the distance in miles, you multiply the given distance in light-years (9.8 x 10^1) by the conversion factor of 5.88 x 10^12 miles per light-year. So, (9.8 x 10^1)(5.88 x 10^12) equals 57.504 x 10^(1+12), which simplifies to 5.76 x 10^14 miles.

15. Expressing 91,910,000 years in scientific notation:
To express this number in scientific notation, you need to adjust the decimal point to have only one digit before the decimal. So, 91,910,000 becomes 9.191 x 10^7 years.

16. Time for radio signal to reach Earth's surface:
To calculate the time, you need to divide the distance traveled (3.6 x 10^7 meters) by the rate (3 x 10^8 meters per second). So, (3.6 x 10^7)/(3 x 10^8) equals 1.2 x 10^(7-8), which simplifies to 1.2 x 10^-1 seconds.

18. Determining if y=6x^7 represents an exponential function:
An exponential function has a variable raised to a constant exponent. In this case, y is raised to the power of 7, which is a constant exponent. Therefore, y=6x^7 does represent an exponential function.

I hope these step-by-step explanations help you understand how to solve these problems and derive the answers.

Looks like you cadges some answers, but need to show your work. I will say that #18 is false. It is most certainly an exponential function. If that is not clear, you really need to do some studying.

Do you have any thoughts at all on these exercises?