Question

What is the value of 'n' in the equation aⁿ/ᵃ³ = a⁹?
a) 3
b) 6
c) 12
d) 27

Answer 1

The value of 'n' in the equation aⁿ/ᵃ³ = a⁹ is n = 12.

Step-by-step explanation:

To find the value of 'n', we can use the property of exponents that states aᵐ/ᵃⁿ =
`a^(m-n). I`n the given equation aⁿ/ᵃ³ = a⁹, applying this exponent property simplifies it to
`a^(n-3)` = a⁹. Setting the exponents equal to each other gives us n - 3 = 9. Solving for 'n' by adding 3 to both sides, we get n = 12.

Therefore, the correct answer is option (c) n = 12. This aligns with the calculation, demonstrating that when n = 12, the equation holds true.

Options (a) 3, (b) 6, and (d) 27 are incorrect, as they do not satisfy the equation. Understanding exponent properties is crucial to manipulate and simplify expressions involving exponents. In this case, recognizing the rule for dividing exponents allows for a straightforward solution to find the value of 'n' that satisfies the equation.