Understanding Exponents and Their Properties

This video tutorial explains how to simplify expressions involving negative exponents by applying known exponent rules. It covers the properties of negative exponents, such as how a base raised to a negative exponent is equal to one divided by that base raised to the positive exponent. The tutorial also demonstrates how to handle fractions with negative exponents and provides example problems to illustrate these concepts.

What is the result of any base raised to the power of zero?

• The base itself

• Zero

• One

• Negative one

How do you simplify a base raised to a negative exponent?

• Multiply by zero

• Divide by the base raised to the positive exponent

• Add the base to itself

• Subtract the base from itself

What is the reciprocal of a fraction c/d?

• c/d

• d/c

• 1/(c*d)

• c*d

What happens to a base with a negative exponent in the numerator?

• It stays in the numerator

• It moves to the denominator with a positive exponent

• It becomes zero

• It becomes negative

In the staircase analogy, what does the key represent?

• The base

• The exponent

• The negative sign

• The positive sign

How do you simplify two to the third raised to the negative third?

• 2^0

• 2^6

• 2^-9

• 2^9

What is a common mistake when dealing with negative exponents?

• Flipping all terms in a fraction

• Adding exponents

• Ignoring the base

• Multiplying exponents

What happens to x^3 in both the numerator and denominator?

• It becomes zero

• It stays as x^3

• It becomes x^6

• It cancels out to one

How do you handle y to the negative third in the denominator?

• Make it zero

• Leave it in the denominator

• Multiply it by itself

• Move it to the numerator with a positive exponent

What is the final result of y^4 times y^3?

• y^1

• y^7

• y^12

• y^0