what rule is 6^-12/9^-15= 9^15/6^12
1. product rule
2. power rule
3. quotient rule
4. negative integer exponent rule
5.zero power rule
3. quotient rule
The correct rule that is used in the equation 6^-12/9^-15 = 9^15/6^12 is the quotient rule.
The rule that applies to the equation 6^(-12) / 9^(-15) = 9^15 / 6^12 is the quotient rule.
To explain how the quotient rule works, we need to understand negative exponents. A negative exponent represents the reciprocal of the base raised to the positive exponent.
In this case, 6^(-12) is equivalent to 1 divided by 6^12, and 9^(-15) is equivalent to 1 divided by 9^15.
Now, let's simplify the equation step by step:
Step 1: Rewrite 6^(-12) and 9^(-15) as fractions using the negative exponent rule:
6^(-12) = 1 / 6^12
9^(-15) = 1 / 9^15
Step 2: Substitute the fractions into the equation:
(1 / 6^12) / (1 / 9^15) = 9^15 / 6^12
Step 3: Apply the quotient rule by dividing the fractions:
(1 / 6^12) * (9^15 / 1) = 9^15 / 6^12
Step 4: Simplify the equation:
9^15 / 6^12 = 9^15 / 6^12
Therefore, the correct rule that applies to this equation is the quotient rule.