Exponents and Their Properties

The video tutorial explains how to simplify mathematical expressions using properties of exponents. It covers converting negative exponents to positive, simplifying fractions with negative exponents, and understanding zero exponents. The tutorial uses examples to demonstrate these concepts, emphasizing the importance of rewriting expressions to have only positive exponents.

What property allows us to change the order of multiplication in an expression?

• Identity Property

• Associative Property

• Distributive Property

• Commutative Property

How do you simplify an expression with a negative exponent?

• Subtract the exponent from the base

• Multiply by zero

• Convert it to a positive exponent by taking the reciprocal

• Add the exponent to the base

What is the simplified form of 18z^-4?

• 1/18z^4

• 18/z^4

• 18z^4

• z^4/18

What is the result of moving a factor with a negative exponent across the fraction bar?

• The exponent doubles

• The exponent becomes positive

• The exponent becomes zero

• The exponent remains negative

What happens to the exponents when you take the reciprocal of a fraction raised to a power?

• The exponents double

• The exponents change sign

• The exponents become zero

• The exponents remain the same

What is the simplified form of 2/3 raised to the power of -3?

• 1/27

• 1/8

• 8/27

• 27/8

What is the result of 3 raised to the power of 3?

• 9

• 27

• 81

• 243

What is the value of any number raised to the power of zero?

• Zero

• Negative one

• The number itself

• One

How do you simplify an expression with a zero exponent?

• Add one to the base

• Convert it to one

• Subtract one from the base

• Multiply by zero

What is the simplified form of 1/x^-5?

• x^5

• 1/x^5

• x^-5

• 5x