Unit 2: Exponents and Scientific Notation
What a repeated-multiplication shorthand buys you, and how it scales all the way from atoms to galaxies.
6 topics · 23 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What Exponents Mean
- How it worksHow does an exponent tell you how many times the base gets multiplied by itself?
- Worked exampleFind the value of 2 to the 5th power and 5 to the 2nd power.
- Going furtherWhat happens to the value of a power when the exponent goes up by just 1?
- Common mistakeWhy doesn't 3 to the 4th power mean 3 times 4?
Your turn1 of 2
A combination lock has 3 dials, and each dial has 5 possible settings. How many different combinations are possible in total?Multiplying and Dividing Powers with the Same Base
- How it worksHow does expanding two powers with the same base into repeated multiplication show why you add exponents when multiplying and subtract them when dividing?
- Worked exampleFind the value of 3 to the 4th power times 3 to the 2nd power, written as a single power of 3.
- Worked exampleFind the value of 5 to the 6th power divided by 5 to the 2nd power, written as a single power of 5.
- Common mistakeWhy doesn't multiplying two powers with the same base mean you multiply the exponents together?
Your turn1 of 2
A scientist counts 7 to the 4 power bacteria in one sample and 7 to the 6 power bacteria in another. Multiplied together, that equals 7 to what power?Negative Exponents
- How it worksHow does dividing by the base one more time turn a positive exponent into a negative one?
- Worked exampleFind the value of 2 to the negative 3rd power.
- Common mistakeWhy doesn't a negative exponent make the whole number negative?
- Going furtherWhat happens to the value of 2 to a negative exponent as the exponent gets more and more negative?
Your turn1 of 2
A photo is shrunk to 1 over 4 of its size, 2 times in a row. What fraction of the original photo size is left, equal to 4 to the negative 2 power?Powers of Ten
- How it worksHow does raising 10 to a power tell you exactly how many zeros follow the 1?
- Worked exampleFind the value of 10 to the 6th power and 10 to the negative 2nd power.
- Worked exampleFind the value of 10 to the 0 power and explain why it isn't 0.
- Going furtherWhat happens to a power of ten's value every time the exponent drops by one?
Your turn1 of 2
The population of a town is written as 10 to the 6 power people. How many people is that?Scientific Notation
- How it worksHow do you convert a huge or tiny number into a decimal between 1 and 10 times a power of ten?
- Worked exampleFind the scientific notation for 45,000,000 and the standard form of 3.2 times 10 to the negative 4th power.
- Common mistakeWhy isn't 45 times 10 to the 6th power already in scientific notation?
Your turn1 of 2
A galaxy is said to have 7 followed by 6 zeros stars (that is, 7 times 10 to some power). What is the exponent on the 10?Order of Operations with Exponents
- How it worksHow does the order of operations tell you to handle an exponent before the multiplication or addition around it?
- Worked exampleFind the value of 4 plus 2 times 3 squared.
- Common mistakeWhy doesn't the negative sign in negative 3 squared get squared along with the 3?
- Going furtherWhat changes about the order of operations once a power sits inside a set of parentheses?
Your turn1 of 2
A garden already has 7 plants. A gardener then adds 4 new square plots, each 5 by 5 plants. How many plants are there in total?