Exponent properties involving products | Numbers and operations | 8th grade | Khan Academy

TL;DR

This video provides a comprehensive review of exponent properties, including how to simplify and multiply expressions with exponents.

Transcript

In this video, I want to do a bunch of examples involving exponent properties. But, before I even do that, let's have a little bit of a review of what an exponent even is. So let's say I had 2 to the third power. You might be tempted to say, oh is that 6? And I would say no, it is not 6. This means 2 times itself, three times. So this is going to b... Read More

Key Insights

• ✖️ Exponents represent repeated multiplication, where the base is multiplied by itself the number of times specified by the exponent.
• ⚾ Multiplying exponents with the same base involves adding the exponents together.
• ✊ Raising a power to another power results in multiplying the exponents.

Questions & Answers

Q: What does 2 to the third power equal?

2 to the third power is equal to 2 multiplied by itself three times, which equals 8.

Q: Can exponents increase rapidly?

Yes, exponents increase rapidly. For example, 5 to the seventh power is a really large number, and 5 to the 17th power would be even more massive.

Q: Why is 3x times 3x times 3x equal to 27x to the third power?

When multiplying the same base raised to the power, the exponents can be added. In this case, 3x times 3x times 3x is equal to 3 to the third power times x to the third power, which simplifies to 27x to the third power.

Q: What property allows us to simplify expressions by multiplying exponents?

The property is based on having the same base and multiplying the exponents. For example, 2 squared times 2 to the fourth can be simplified to 2 to the 2 plus 4 power, which is equal to 2 to the 6th power.

Summary & Key Takeaways

• The video starts with a review of what an exponent is and provides examples of evaluating exponents, emphasizing the repeated multiplication involved.

• The video introduces exponent properties such as multiplying exponents with the same base, adding exponents with the same base, and raising a power to another power.

• The video concludes with examples of simplifying expressions with exponents using the properties discussed.