Final answer:
The expression ((a³)/(b⁵))⁵ simplifies to (a / b)¹⁵ by multiplying the exponents of a and b within the numerator and the denominator respectively.
Step-by-step explanation:
To simplify the expression ((a³)/(b⁵))⁵, we need to apply the rules of exponents. This process involves raising both the numerator and the denominator to the fifth power, resulting in a new expression with the exponents multiplied.
Following the Division of Exponentials rule, which states that we can subtract the exponents when dividing two exponential terms with the same base, we simplify as follows:
(a³)⁵ / (b⁵)⁵ = a³*5 / b⁵*5 = a¹⁵ / b¹⁵
Now, since we have the same exponent for both a and b, we can write this expression as: (a / b)¹⁵
Therefore, the expression ((a³)/(b⁵))⁵ simplifies to (a / b)¹⁵.