Multiplying & dividing powers (integer exponents) | Mathematics I | High School Math | Khan Academy

TL;DR

Multiplying or dividing numbers with the same base and different integer exponents can be simplified by applying the rules of exponent properties.

Transcript

• [Narrator] Let's get some practice with our exponent properties, especially when we have integer exponents. So, let's think about what four to the negative three times four to the fifth power is going to be equal to. And I encourage you to pause the video and think about it on your own. Well there's a couple of ways to do this. See look, I'm mult... Read More

Key Insights

• 😑 Exponent properties allow us to simplify expressions with the same base and different exponents.
• ⚾ Multiplication of numbers with the same base requires adding the exponents, while division requires subtracting the exponents.
• 🔁 Exponent properties can be understood intuitively by considering them as repeated multiplication or division.
• 😑 The simplified expression after applying the exponent properties can be expressed in terms of positive exponents or as fractions.
• ✊ Understanding the concept of exponent properties is essential for solving mathematical problems involving powers and exponents.
• 📏 The rules for exponent properties are consistent regardless of whether the exponents are positive or negative integers.
• 🤩 The key to simplifying expressions with exponents is identifying the base and applying the appropriate exponent rules.

Questions & Answers

Q: How can you simplify the expression 4^(-3) * 4^5?

By applying the rule of exponent properties, we can add the exponents and simplify it to 4^2, which is equal to 16.

Q: What is the result of A^(-4) * A^2?

The same base A is being multiplied, so we can add the exponents and simplify it to A^(-2), which can be written as 1/A^2.

Q: How can you simplify 12^(-7) divided by 12^(-5)?

By applying the rule of exponent properties for division, subtract the exponents to get 12^(-2), which is equal to 1/12^2 or 1/144.

Q: When dividing X^(-20) by X^5, what is the simplified expression?

By subtracting the exponents, we can simplify it to X^(-25), which is the same as 1/X^25.

Summary & Key Takeaways

• When multiplying numbers with the same base and different exponents, simply add the exponents.

• When dividing numbers with the same base and different exponents, subtract the exponents.

• The rules of exponent properties can be intuitively understood by considering them as repeated multiplication or division.