Exponents and Their Properties

This video tutorial explains how to multiply exponents with different bases and exponents. It covers methods to rewrite numbers to have the same base or exponent, allowing for simplification. The video includes examples with positive and negative exponents, demonstrating how to handle each case. It also addresses situations with prime bases and provides strategies for simplifying expressions by changing exponents. The tutorial aims to help viewers understand the pattern and logic behind exponent multiplication.

What is the main topic of the video?

• Adding exponents with the same base

• Multiplying exponents with different bases and exponents

• Dividing exponents with different bases

• Subtracting exponents with the same base

What is the first step in multiplying exponents with different bases?

• Add the exponents

• Rewrite one number to match the other

• Divide the exponents

• Subtract the exponents

In Example 1, how is 4 rewritten to have the same base as 2?

• 4 is rewritten as 2^5

• 4 is rewritten as 2^2

• 4 is rewritten as 2^3

• 4 is rewritten as 2^4

What is the result of 2^10 * 2^3?

• 2^15

• 2^7

• 2^30

• 2^13

In Example 2, how is 27 rewritten to have the same base as 3?

• 27 is rewritten as 3^3

• 27 is rewritten as 3^2

• 27 is rewritten as 3^4

• 27 is rewritten as 3^5

What is the result of 3^8 * 3^-6?

• 3^4

• 3^2

• 3^14

• 3^12

In Example 3, how is 81 rewritten to have the same base as 9?

• 81 is rewritten as 9^4

• 81 is rewritten as 9^2

• 81 is rewritten as 9^3

• 81 is rewritten as 9^5

What is the result of 9^-5 * 9^4?

• 9^-1

• 9^1

• 9^0

• 9^2

What should you do if you have a negative exponent?

• Place the base in the denominator

• Subtract 1 from the exponent

• Multiply the base by 2

• Add 1 to the exponent

What is the final result of 9^-1?

• 1/9

• 9

• 0

• 9^1