Question

Select all of the expressions that are equivalent to 5^3/5^-2.

a. 3125
b. 5^1
c. 1/5
d. 5
e. 5^5
f. 5^-1
Answer
Select all of the expressions that are equivalent to (2/3)^-4.

a. (-2/3)^4
b. -16/81
c. (3/2)^4
d. 2*-4/3*-4
e. 81/16
f. 8/12
g. 3*3*3*3/2*2*2*2
h. -2*2*2*2/3*3*3*3
Answer
The earth weighs 5.972 * 10^24 kilos (1.31660063 x 10^25 lbs). A penny weighs 3.1*10^-3 kilos (6.83433013*10^-3 lbs). APPROXIMATELY how many pennies weigh as much as the earth?

Use WHOLE numbers only. No decimal places allowed. Use kilograms.
Answer
Decimals do not count as the final answer. They are not whole numbers, so please exclude them.
Answered by GPT 3.5
To simplify the expression 5^3/5^-2, we can subtract the exponents.

5^3/5^-2 = 5^(3-(-2)) = 5^5

Therefore, the equivalent expressions are:

a. 3125
e. 5^5
Answered by GPT 3.5
To simplify the expression (2/3)^-4, we can apply the rule that states that a negative exponent is equivalent to its reciprocal raised to the positive version of the exponent.

(2/3)^-4 = (3/2)^4

Therefore, the equivalent expressions are:

c. (3/2)^4
Answered by GPT 3.5
To find out how many pennies weigh as much as the Earth, we need to divide the mass of the Earth by the mass of a single penny.

Mass of the Earth = 5.972 * 10^24 kilos
Mass of a penny = 3.1 * 10^-3 kilos

To obtain a whole number answer, we need to find the closest whole number value to the ratio of the Earth's mass to that of a penny.

Number of pennies = (Mass of the Earth) / (Mass of a penny)

Number of pennies = (5.972 * 10^24) / (3.1 * 10^-3)

As the number of pennies is likely to be large, I will use scientific notation to represent the final answer.

Number of pennies = 1.92418672 x 10^27

Therefore, approximately 1.92418672 x 10^27 pennies weigh as much as the Earth.
Answered by GPT 3.5
I apologize for the confusion. To find the approximate number of pennies, we can divide the mass of the Earth by the mass of a single penny and round down to the nearest whole number.

Number of pennies = (Mass of the Earth) / (Mass of a penny)
Number of pennies = (5.972 * 10^24) / (3.1 * 10^-3)

To simplify the calculation, we can divide the coefficients separately and subtract the exponents:

Number of pennies ≈ (5.972 / 3.1) * 10^(24 - (-3))

The division of the coefficients is approximately 1.9290322581.

Number of pennies ≈ 1.9290322581 * 10^(24 + 3)

The sum of the two exponents is 27.

Number of pennies ≈ 1.9290322581 * 10^27

Therefore, approximately 1.9290322581 * 10^27 pennies weigh as much as the Earth.