Understanding Negative Exponents

The video tutorial explains why raising a number to a negative exponent is equivalent to taking the reciprocal of that number raised to the positive exponent. It uses powers of 2 to illustrate the concept, showing how decrementing the exponent by 1 results in division by 2. The tutorial also covers why any nonzero number raised to the power of zero equals 1, and it emphasizes the reciprocal relationship inherent in negative exponents.

What is the equivalent expression for a number raised to a negative exponent?

• The number itself

• Zero

• The reciprocal of the number raised to the positive exponent

• The number raised to the positive exponent

What is 2 to the third power?

• 6

• 4

• 10

• 8

How do you transition from 2 to the third power to 2 to the second power?

• Multiply by 2

• Add 2

• Subtract 2

• Divide by 2

What is the value of 2 to the 0-th power?

• 1

• Undefined

• 0

• 2

Why is any nonzero number to the 0-th power defined as 1?

• Because it is a mathematical rule

• Because it is undefined

• Because it follows the pattern of division by the base

• Because it is always zero

What is 2 to the negative 1 power?

• 2

• 1

• 0

• 1/2

What is the relationship between 2 to the negative 1 and 2 to the 1?

• They are equal

• They are reciprocals

• They are both zero

• They are both negative

What is 2 to the negative 2 power?

• 2

• 1/2

• 4

• 1/4

What pattern is observed when calculating negative exponents?

• Multiplying by the base

• Adding the base

• Dividing by the base

• Subtracting the base

What is 2 to the negative 3 power?

• 1/8

• 1/2

• 8

• 1/4