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100^1/3

Answer

The answer to 100 raised to the power of 1/3 is 10. This is because raising a number to a fractional power is the same as taking the root of the number.

Calculating the Root of a Number

To calculate the root of a number, you divide the exponent by the root number. For example, to calculate the cube root of 10, you would divide 3 (the exponent) by 3 (the root number), which is 1. This means the cube root of 10 is 10^1.

Calculating the Fractional Power of a Number

To calculate the fractional power of a number, you divide the exponent by the root number. For example, to calculate the power of 10 with an exponent of 1/3, you would divide 1 (the exponent) by 3 (the root number), which is 1/3. This means the power of 10 with an exponent of 1/3 is 10^1/3.

Calculating the Fractional Power of a Number with an Exponent of 1

To calculate the fractional power of a number with an exponent of 1, you simply take the root of the number. For example, to calculate the power of 10 with an exponent of 1/3, you would take the cube root of 10, which is 10^1. This means the power of 10 with an exponent of 1/3 is 10^1/3, which is equal to 10.

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Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium.

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium. Explain your answers in details

Suppose 20 households in a community have the demand function Q = 2 – 0.001P each for streetlights while 5 other households have the demand function Q = 3 – 0.002P each for streetlights. Here, Q refers to the number of streetlights to erect near their home while P is the unit price of each streetlight. The cost of building each streetlight is GHS 45. a) Assuming each household is making its separate purchase decision, find the market demand function for streetlights for all 25 households b) Assuming each household is making its separate purchase decision, find the equilibrium price and number of streetlights in the community c) Assuming a community association has decided to coordinate this streetlight purchase decision problem. The community leader uses the demand functions to determine how much each household is willing to contribute (willingness to pay) towards the first, second, third, etc streetlight. The first light is purchased only when the sum of individual households’ contributions is at least equal to the marginal cost of streetlights. Find out how many streetlights are purchased for this community in equilibrium.

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