Mastering Multiplication and Division of Powers

This video tutorial explains how to multiply and divide numbers with powers, focusing on cases where the numbers have the same base. It covers the rules for multiplication and division of powers, provides examples, and offers shortcuts for simplifying expressions. The video also includes practice questions and advanced examples involving negative powers and multiple terms. Finally, it discusses handling powers with both numbers and letters separately.

What is the first requirement for the rules of multiplying and dividing powers to work?

• The numbers must have the same base.

• The numbers must be prime.

• The numbers must be odd.

• The numbers must be even.

What does b^3 * b^2 simplify to?

• b^7

• b^4

• b^5

• b^6

What is the shortcut for multiplying powers?

• Divide the exponents.

• Subtract the exponents.

• Multiply the exponents.

• Add the exponents.

How do you simplify a^6 / a^3?

• a^1

• a^2

• a^3

• a^9

What is the shortcut for dividing powers?

• Add the exponents.

• Multiply the exponents.

• Divide the exponents.

• Subtract the exponents.

What is x^7 * x^4?

• x^10

• x^11

• x^12

• x^9

What is 2^7 / 2^4?

• 2^2

• 2^4

• 2^3

• 2^1

What is a^9 * a^-5?

• a^4

• a^14

• a^3

• a^5

How do you handle terms with both numbers and letters when multiplying?

• Divide the numbers and subtract the exponents of the letters.

• Subtract the numbers and add the exponents of the letters.

• Add the numbers and multiply the exponents of the letters.

• Multiply the numbers and add the exponents of the letters.

What is the result of 8b^11 / 2b^5?

• 4b^6

• 4b^5

• 8b^6

• 6b^6