Video: Solving Word Problems by Evaluating and Comparing Numbers with Nonnegative Integer Exponents

A football stadium has 16⁴ seats, and a cricket stadium has 5⁷ seats. Which stadium has more seats? How many more?

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Video Transcript

A football stadium has 16 to the power of four seats, and a cricket stadium has five to the power of seven seats. Which stadium has more seats? How many more?

The number of seats in the football stadium was equal to 16 to the power of four. As the power or exponent is four, we need to multiply 16 by 16 by 16 and by 16 again. There are four 16s. It is important to note that this is not the same as 16 times four as this would give us an answer of 64. 16 to the power four is equal to 65536.

The cricket stadium had five to the power of seven seats. We can calculate this by multiplying five by five by five by five by five by five and by five again. There are seven fives. This is because the exponent or power was equal to seven. Five to the power of seven is equal to 78125.

We’ve, therefore, answered the first part of the question. The cricket stadium has more seats as 78125 is greater than 65536.

The second part of our question asked us to work out how many more seats the stadium had. In order to do this, we subtract 65536 from 78125. We need to work out the difference between the two numbers. 78125 minus 65536 is equal to 12589.

We can, therefore, say that the cricket stadium has 12589 more seats than the football stadium. Five to the power of seven is 12589 more than 16 to the power of four.

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