Final answer:
The value of x when 9⁵ is written in the form 3ˣ is found by expressing 9 as 3², then applying the rule of exponents to get (3²)⁵, which simplifies to 3ˣ·. Thus, x equals 10.
Step-by-step explanation:
To find the value of x when 9⁵ is written in the form 3ˣ, we must first express 9 as a power of 3. Since 9 is equal to 3², we can rewrite 9⁵ as (3²)⁵. Using the multiplication rule of exponents, which states that (xᴇ)ᴇ = xˣ.·, we can multiply the exponents together.
Applying this rule, (3²)⁵ becomes 3⁴⁰ (2 multiplied by 5). Therefore, the exponent x is equal to 10. So, the solution to the problem is x = 10. This solution demonstrates the significance of understanding exponent rules to simplify and solve expressions involving powers.