Exploring the Product of Powers Property

The video tutorial introduces the product of powers property, explaining how to multiply terms with the same base by adding their exponents. It provides examples using numbers and variables, demonstrating the rule's application. The tutorial also covers more complex problems, emphasizing the commutative property of multiplication and the importance of recognizing when terms can be combined. The video concludes with a challenge involving distribution and addition, highlighting the limitations of the product of powers rule.

What is the result of multiplying 2 squared by 2 cubed?

• 8

• 2 to the power of 6

• 4 to the power of 5

• 2 to the power of 5

When multiplying x cubed by x to the fourth, the result is x to the power of?

• x squared

• x to the 7th power

• 12

• 7

What is the general rule for multiplying terms with the same base?

• Multiply the exponents

• Divide the exponents

• Add the exponents

• Subtract the exponents

What is the simplified form of x cubed times x to the fifth times x to the fourth?

• x cubed

• x to the 13th power

• x to the 12th power

• x to the 9th power

In the expression y to the 5th times 2 times y to the 9th, what does it simplify to?

• 2y to the 14th

• y to the 14th

• 2y to the 9th

• y to the 7th

What is the result of simplifying x squared y to the fifth times x to the fourth y to the ninth?

• x to the 6th y to the 14th

• x to the 9th y to the 5th

• x squared y to the ninth

• x to the 4th y to the 14th

How do you simplify the expression 2y to the 5th times y to the 9th?

• y to the 14th

• 2y to the 9th

• 2y to the 14th

• y to the 5th

What is the simplified form of 2 times 3 times a times a cubed?

• 6a cubed

• 9a

• 5a to the fourth

• 6a to the fourth

What does 2 times a times b squared times b cubed simplify to?

• 2ab to the 5th power

• 2ab to the 5th

• 2b to the 5th

• 2a to the 5th b to the 5th

What is the result of distributing a outside the parentheses in a(2ab cubed + 5a to the fourth b squared)?

• 2ab cubed + 5a to the fourth b squared

• a squared b cubed + a to the fifth b squared

• 7a to the fifth b to the fifth

• 2a squared b cubed + 5a to the fifth b squared