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
1. To solve -(5)^-1, we can rewrite it as -1/(5^1). The negative sign in front means we need to take the reciprocal of the value. So, -(5)^-1 is equal to -1/5.
3. To simplify -1/y^-4, we can multiply the numerator and denominator by y^4 to get rid of the negative exponent. This gives us -1 * y^4 / 1. Multiplying a number by its reciprocal gives us 1, so the answer simplifies to -y^4.
4. To solve 5^4 x 5^7, we can add the exponents when multiplying powers with the same base. So, 5^4 x 5^7 = 5^(4+7) = 5^11.
7. To simplify (5t^3)^-4, we can apply the exponent to both the base and the exponent in parentheses. This gives us 1 / (5^4 x t^(3*4)), which simplifies to 1 / (625t^12). Therefore, the answer is 1/625t^12.
12. To determine the order of the given numbers, we look at the powers of 10. Smaller powers of 10 come first, so the order is 7 x 10^-9, 4 x 10^-7, 1 x 10^4, 2 x 10^4.
13. To simplify (8 x 10^4)(9 x 10^-8), we multiply the coefficients and add the exponents of 10. So, (8 x 9) x 10^(4 + -8) = 72 x 10^-4 = 7.2 x 10^-3.
14. To find the approximate number of miles for a distance given in light-years, we multiply the light-year distance by the conversion factor of 5.88 x 10^12 miles per light-year. So, (9.8 x 10^1) x (5.88 x 10^12) = 57.504 x 10^13 = 5.76 x 10^14 miles.
15. To express 91,910,000 years in scientific notation with the highest level of precision, we move the decimal point until there is only one non-zero digit before it. This gives us 9.191 x 10^7.
16. To calculate the time it takes for a radio signal to travel from a satellite to Earth's surface, we divide the distance (3.6 x 10^7 meters) by the rate of travel (3 x 10^8 meters/second). So, (3.6 x 10^7) / (3 x 10^8) = 1.2 x 10^(-1) seconds.
18. An exponential function is generally of the form y = ab^x, where a and b are constants. The given expression, y = 6x^7, includes a variable raised to a constant exponent, but it is not in the form of an exponential function. Therefore, the rule y=6x^7 does not represent an exponential function.