Match the proper exponent rule (law) below
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5 points
(a/b)^m = a^m b^m a^0 = 1 (a^m)^n = a^mn a^m x a^n = a ^ m +n (a/b)^m = a ^ m-n
Quotient Rule
Product Rule
Power of a quotient
Zero Expoent Law
Power of a Power
Quotient Rule
Product Rule
Power of a quotient
Zero Expoent Law
Power of a Power
Quotient Rule: (a/b)^m = a^m b^m
Product Rule: a^m x a^n = a^m+n
Power of a quotient: (a/b)^m = a^m-n
Zero Exponent Law: a^0 = 1
Power of a Power: (a^m)^n = a^mn
Match the proper exponent rule (law) below:
(a/b)^m = a^m b^m - Power of a quotient
a^0 = 1 - Zero Exponent Law
(a^m)^n = a^mn - Power of a Power
a^m x a^n = a ^ m +n - Product Rule
To match the proper exponent rule to the corresponding law, we need to understand the definitions of each rule.
1. Quotient Rule: (a/b)^m = a^m / b^m
This rule states that when you have a fraction raised to a power, you can distribute that power to both the numerator and denominator by raising each separately.
2. Product Rule: a^m x a^n = a^(m + n)
This rule states that when you multiply two variables with the same base raised to different powers, you can add the powers together.
3. Power of a quotient: (a/b)^m = a^m / b^m
This rule is the same as the Quotient Rule mentioned above.
4. Zero Exponent Law: a^0 = 1
This rule states that any number raised to the power of zero is equal to 1.
5. Power of a Power: (a^m)^n = a^(m x n)
This rule states that when you have an exponent raised to another exponent, you can multiply the exponents together.
Based on these definitions, we can match the given exponent rules:
(a/b)^m = a^m b^m - Power of a quotient
a^0 = 1 - Zero Exponent Law
(a^m)^n = a^mn - Power of a Power
a^m x a^n = a^(m + n) - Product Rule
(a/b)^m = a^(m - n) - Not mentioned in provided options
Therefore, the matching is as follows:
Quotient Rule - (a/b)^m = a^m / b^m
Product Rule - a^m x a^n = a^(m + n)
Power of a quotient - Not mentioned in the provided options
Zero Exponent Law - a^0 = 1
Power of a Power - (a^m)^n = a^(m x n)