Integer Exponents Worksheets Grade 8

1. (5³ × 2⁴) ÷ (5² × 2²) = ?
2. Aroha is designing a series of nested cubes for an art project. The side length of the smallest cube is 3^2 cm. The side length of the next cube is (3^2)^3 cm, and the side length of the largest cube is 3^7 cm. Aroha wants to know how many times the volume of the largest cube is compared to the volume of the smallest cube. What is that ratio? Express your answer as a single power of 3.
3. A rectangular prism has dimensions of 3 × 10⁴ cm by 2 × 10² cm by 5 × 10³ cm. Using the properties of exponents, calculate the volume of the prism in scientific notation.

…and 5 more problems

1. A scientist is studying bacterial growth in a lab. The bacteria population starts with 2,000 cells and doubles every hour. After 5 hours, the scientist needs to express the final population in scientific notation. What is the population of bacteria after 5 hours, written in proper scientific notation?
2. A scientist is studying bacterial growth in a lab. The bacteria population starts with 2^3 cells and doubles every hour according to the pattern 2^(3+n), where n is the number of hours. After 4 hours, the scientist adds a nutrient that multiplies the current population by 2^5 cells. What is the total number of bacteria cells after this nutrient is added? Express your answer in exponential form with a single base.
3. A rectangular solar panel has dimensions of 8.4 × 10^3 millimeters by 3.6 × 10^2 millimeters. What is the area of the solar panel in square millimeters, expressed in standard scientific notation?

…and 4 more problems

1. A rectangular prism has dimensions of 6 × 10² meters by 3 × 10³ meters by 2 × 10¹ meters. Using the properties of exponents, calculate the volume of the prism in scientific notation.
2. (6⁴ × 6⁻²) ÷ (6³ × 6⁻⁴) = ?
3. (5³ × 5⁻²) ÷ (5² × 5⁻⁴) = ?

…and 5 more problems