Question

Andrew and Elena knew that after 28 days they would have 2^28 coins, but they wanted to find out how many coins that actually is Andrew wrote: 2^28=2×28=56. Elena said, " No, exponents mean repeated multiplication. It should be 28×28, which works out to be 784." Do you agree with either of them? Explain your reasoning.

Answer 1

Both Andrew and Elena are wrong. The actual value of 2^28 equals 268,435,456.

Explanation:

Elena was right when she said exponents mean repeated multiplication but she accidentally calculated the value of 28^2 instead of 2^28. 2^28 means that the number 2 should be multiplied with itself for 28 times.

2^2 means 2 multiplied by 2 equals 4. 2^3 means 2 multiplied by 2 and then multiplied by 2 again which equals 8. Similarly, if you multiply 2 with itself 28 times you will get a value of 268,435,456 (two hundred and sixty-eight million, four hundred and thirty-five thousand, four hundred and fifty-six). So Andrew and Elena will have 268,435,456 coins after 28 days.