Faced with the problem of dividing 524 by 58, Brook is having trouble deciding which of these four answers is correct: 516, 53, 116, or 13. Your help is needed. Once you have answered Brook’s question, experiment with other examples of this type until you are ready to formulate the common-base principle for division that tells how to divide bm by bn and get another power of b. Then apply this principle to the following situations: (a) Earth’s human population is roughly 6 × 109, and its total land area, excluding the polar caps, is roughly 5 × 107 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 × 108 meters per second, how many seconds does it take for the Sun’s light to travel 1.5 × 1011 meters to Earth?