Faced with the problem of dividing 5^24 by 5^8, Brook is having trouble deciding which of these four answers is correct: 5^16, 5^3, 1^16, or 1^3. Your assistance is needed. Once you have answered Brook’s question, experiment with other examples of this type until you can formulate the common-base principle for division of exponential expressions. Then apply this principle to the following situations:
(a) Earth’s human population is roughly 6 x 10^9, and its total land area excluding the polar caps is roughly 5 x 10^7 square miles. If the human population were distributed uniformly over all available land, approximately how many persons would be found per square mile?
(b) At the speed of light, which is 3 x 10^8 meters per second, how many seconds does it take for the Sun’s light to travel the 1.5 x 10^11 meters to Earth?
Thanks!
(a) Earth’s human population is roughly 6 x 10^9, and its total land area excluding the polar caps is roughly 5 x 10^7 square miles. If the human population were distributed uniformly over all available land, approximately how many persons would be found per square mile?
(b) At the speed of light, which is 3 x 10^8 meters per second, how many seconds does it take for the Sun’s light to travel the 1.5 x 10^11 meters to Earth?
Thanks!
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5²⁴/5⁸ = 5²⁴⁻⁸ = 5¹⁶
:::::
people per square mile = total people/total area
= (6×10⁹)/(5×10⁷)
= (6×10⁹⁻⁷)/5
= (6/5)×10²
= 1.2×10²
= 120
:::::
(1.5×10¹¹ meters)/(3×10⁸ meters/second) = (1.5/3)×10¹¹⁻⁸
= 0.5×10³
= 500 seconds
:::::
people per square mile = total people/total area
= (6×10⁹)/(5×10⁷)
= (6×10⁹⁻⁷)/5
= (6/5)×10²
= 1.2×10²
= 120
:::::
(1.5×10¹¹ meters)/(3×10⁸ meters/second) = (1.5/3)×10¹¹⁻⁸
= 0.5×10³
= 500 seconds