Final answer:
a = 6
The missing exponent 'a' in the equation n³ = nˣ * n⁻³ is found using the properties of exponents. After isolating 'a', it is determined that a = 6.
Step-by-step explanation:
The question asks to find the missing exponent in the equation n³ = nˣ * n⁻³. To find the missing exponent 'a', we can use the properties of exponents which state that when we multiply exponential expressions with the same base, we add the exponents. Since the base 'n' is the same on both sides, we can equate the sum of exponents on the right-hand side to the exponent on the left-hand side which is 3.
Using the rule, we get:
3 = a + (-3)
Adding 3 to both sides to isolate 'a', we get:
a = 3 + 3
a = 6
Therefore, the missing exponent 'a' is 6.