Product of Powers Property (Example)

The video tutorial explains how to simplify expressions with different bases using the product of powers and commutative properties. It demonstrates rearranging factors to group similar bases together, allowing for the addition of exponents. The final expression is simplified to m to the 9th power times n to the 5th power, with an explanation that multiplication symbols are not needed between powers.

What is the main reason we cannot add exponents of different bases directly?

• Because they have different bases

• Because they are not in the same equation

• Because they are not whole numbers

• Because they have different coefficients

What property allows us to rearrange the factors in an expression?

• Associative Property

• Identity Property

• Distributive Property

• Commutative Property

After rearranging the expression, what is the new order of the terms?

• m to the 5th times m to the 4th times n-squared times n-cubed

• m to the 4th times m to the 5th times n-cubed times n-squared

• n-cubed times n-squared times m to the 4th times m to the 5th

• m to the 4th times n-cubed times m to the 5th times n-squared

How do you simplify the expression m to the 4th times m to the 5th?

• m to the 20th

• m to the 8th

• m to the 9th

• m to the 1st

Why is it unnecessary to write the multiplication symbol between m to the 9th and n to the 5th?

• Because they are different bases

• Because they are in the same equation

• Because it is a mathematical rule

• Because two powers written next to each other imply multiplication