Understanding Negative Exponents

The video explains why a number raised to the power of negative one equals one divided by that number, provided the base is not zero. It uses base 3 to demonstrate the pattern of decreasing exponents and how dividing by the base results in the next lower power. The video also covers the quotient property of exponents, showing how to simplify expressions by subtracting exponents. Two justifications for the negative exponent rule are provided: pattern recognition and the quotient property.

What is the value of a raised to the power of negative one when a is not zero?

• 0

• -a

• 1/a

• a

If 3 to the power of 5 is 243, what is 3 to the power of 4?

• 243

• 81

• 27

• 9

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

• 1/3

• 1/9

• 1/27

• 1/6

How can you simplify the expression 3 cubed divided by 3 squared using the quotient property?

• 1

• 3

• 9

• 27

What is the quotient property of exponents?

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• a^m + a^n = a^(m+n)

• a^m - a^n = a^(m-n)

What is the result of 3 squared divided by 3 cubed?

• 3

• 1/3

• 9

• 1

If you expand and simplify 3 squared divided by 3 cubed, what do you get?

• 1/3

• 1

• 9

• 3

What is the value of 3 raised to the power of negative one?

• 3

• 1/3

• 1

• 9

How does the quotient property help in understanding negative exponents?

• It shows that subtraction of powers results in negative exponents

• It shows that addition of powers results in negative exponents

• It shows that multiplication of powers results in negative exponents

• It shows that division of powers results in negative exponents

What is the general rule for a raised to the power of negative n?

• a^n

• -a^n

• a^(-n)

• 1/a^n