Anthony scored two to the power of seven points in a board game and Noah scored seven to the power of two points. Determine who won the game and by how many points.
So we’ve been given both Anthony and Noah’s scores expressed in terms of powers: two to the power of seven and seven to the power of two. In order to work out who won the game, we need to evaluate what each of these numbers are equal to.
Let’s start with Anthony. Two to the power of seven means two multiplied by itself seven times: two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two. To evaluate this, we just keep doubling two. Two multiplied by two or two squared is four. Doubling this gives two cubed, which is eight. Doubling again gives two to the power of four, which is 16. Doubling 16 gives two to the power of five — 32. Doubling 32 gives two to the power of six, which is 64. Doubling one final time gives the value of two to the power of seven — 128. So we’ve worked out how many points Anthony scored. Two to the power of seven is equal to 128.
Now, let’s consider how many points Noah scored. Seven to the power of two or seven squared is equal to seven multiplied by seven two times. This is equal to 49. So now, we know that Noah has scored 49 points.
The person who won the game is the person who scored more points. So this person is Anthony. To work out by how many points Anthony won the game, we just need to subtract Noah’s score from Anthony’s. 128 minus 49 is equal to 79.
So evaluating both powers shows us that Antony won the game by 79 points.