Final answer:
The student is asked to find the missing exponent in the equation 3ˀ * 3⁻⁶ = 3². To solve for the missing exponent, we use exponent properties, specifically that when we multiply like bases, we add the exponents. Thus, the missing exponent is 8, making the complete equation 3⁸ * 3⁻⁶ = 3².
Step-by-step explanation:
In the equation 3ˀ * 3⁻⁶ = 3², we are looking for the missing exponent that would complete the equation accurately. We can use the properties of exponents to solve for the missing variable. One important property is that when multiplying exponential expressions with the same base, we add the exponents:
3ˀ * 3⁻⁶ = 3(ˀ⁻⁶).
To find the value of ˀ that satisfies the equation, we can set up the equation:
ˀ⁻⁶ = 2.
Since we already know that 3⁻⁶ is on the left side of the equation and 3² on the right, the missing exponent must be ˀ = 2 + 6 = 8. Therefore, the complete equation is:
3⁸ * 3⁻⁶ = 3².
Knowing the rules for manipulating exponents can simplify the process of solving such exponent equations.