Integer Exponents Worksheets Grade 8

1. Liam is studying the growth of algae in a pond. He starts with an initial population of 1.6 × 10^4 algae cells. The population triples every day. After 3 days, a chemical treatment is applied that reduces the population to one-twenty-seventh of its current size. What is the final population of algae cells? Express your answer in proper scientific notation.
2. (5³ × 5⁻²) ÷ (5² × 5⁻⁴) = ?
3. A scientist is studying bacterial growth in a lab. The initial population is 500 bacteria, and it doubles every 3 hours. The scientist uses the formula P = 500 × 2^(t/3) to model the population after t hours. If the experiment runs for 12 hours, what will be the total population of bacteria? Express your answer as a whole number.

…and 5 more problems

1. (3⁵ × 3⁻³) ÷ (3² × 3⁻¹) = ?
2. (7⁵ × 7⁻³) ÷ (7² × 7⁻⁴) = ?
3. Aroha is helping her school's science club build a model of a solar system. They have a scale where the distance from the Sun to Neptune is represented as 7.2 × 10⁹ kilometers. The distance from the Sun to Earth is 1.5 × 10⁸ kilometers. How many times farther is Neptune from the Sun compared to Earth? Express your answer as a whole number.

…and 5 more problems

1. Isabella is helping her school's astronomy club build a model of a galaxy. The model shows that a certain star cluster has an initial brightness of 8^4 lumens. As the cluster ages, its brightness increases by a factor of 8^5 every million years. After 3 million years, the cluster undergoes a supernova event that multiplies its current brightness by (8^2)^3. What is the final brightness of the star cluster in exponential form with a base of 8?
2. Emma is designing a rectangular garden for her school project. The length of the garden is 7^3 centimeters and the width is 7^5 centimeters. She wants to cover the entire garden with soil. What is the area of the garden in square centimeters? Express your answer as a power of 7.
3. (8³ × 4⁻²) ÷ (2⁵ × 2⁻³) = ?

…and 5 more problems