Exponent Laws: Real-Life Applications of Powers and Quotients

A gardener is planting flowers in a rectangular garden. If the area of the garden is represented by x^4 square meters, and the length is x^2 meters, what is the width of the garden in terms of x?

• x^3

• x^4

• x^2

• x

A scientist is studying bacteria growth. If the number of bacteria doubles every hour, and after 3 hours the population is represented as 2^3, how many bacteria are there after 5 hours?

• 16

• 64

• 32

• 8

A computer programmer is analyzing code efficiency. If a function runs in x^5 milliseconds and is optimized to run in x^2 milliseconds, how many times faster is the optimized function compared to the original?

• x^3

• x^4

• x^1

• x^6

A factory produces x^6 toys in a day. If they reduce production by half, how many toys do they produce in terms of x?

• 2x^6

• x^6 - 1

• x^6 / 2

• x^6

A car travels at a speed of x^3 kilometers per hour. If it travels for x^2 hours, how far does it travel in terms of x?

• x^4

• x^6

• x^3

• x^5

A recipe calls for x^4 grams of sugar. If you want to make a batch that is 3 times larger, how much sugar do you need in terms of x?

• x^4

• 6x^4

• 3x^2

• 3x^4

A cell phone plan offers x^5 gigabytes of data. If you use x^3 gigabytes in a month, how much data do you have left in terms of x?

• x^3(x^2 + 1)

• x^5 - x^3(x^2)

• x^3(x^2 - 1)

• x^5 - x^3

A book has x^4 pages. If you read x^2 pages a day, how many days will it take to finish the book in terms of x?

• x^2

• x

• x^4

• x^3

A video game has x^3 levels. If you complete x^2 levels in one session, how many levels are left to complete in terms of x?

• x^3 - x

• x^2 + x

• x^2(x - 1)

• x^3 - x^2

A factory produces x^5 units of a product. If they decide to cut production by a factor of x^2, how many units will they produce now in terms of x?

• x^2

• x^5

• x^3

• x^4