Exponent Rules and Properties

This lesson explores exponent patterns with bases other than ten, focusing on zero and negative exponents. It includes activities on comparing expressions and applying exponent rules to different bases. The lesson concludes with a summary of how these rules apply universally, regardless of the base.

Which statement is true about the expression 3^5 compared to 4^6?

• 3^5 is greater than 4^6

• 3^5 is equal to 4^6

• 3^5 is less than 4^6

• 3^5 and 4^6 cannot be compared

What happens when you square a negative number?

• The result is zero

• The result is always negative

• The result is the same as the original number

• The result is always positive

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

• One

• Negative one

• The number itself

• Zero

How can 2^-6 be expressed as a fraction?

• 1/64

• 64

• 1/32

• 32

What is the fractional representation of 5^-3?

• 1/25

• 1/5

• 1/15

• 1/125

In the context of exponent rules, what is the result of multiplying 10^n by 10^m?

• 10^(n-m)

• 10^(n+m)

• 10^(n*m)

• 10^(n/m)

Which expression is not equivalent to 5^-9?

• 5^9

• 5^-3 * 5^-6

• 5^3 * 5^-12

• -5^9

What is a common mistake when dealing with exponents in division?

• Dividing the exponents

• Subtracting the exponents

• Adding the exponents

• Multiplying the exponents

How do exponent rules apply when the base is not ten?

• They apply in the same way

• They apply differently

• They do not apply

• They apply only to positive exponents

Why is it important to keep bases the same when applying exponent rules?

• To simplify calculations

• To ensure the rules apply correctly

• To avoid negative results

• To make the base ten