Answer:
Value of a = 9 (perfect cube)
Explanation:
To make the expression a perfect cube, we need to ensure that each exponent of the prime factors (2, 3, and 5) is a multiple of 3.
The given expression is:
2⁹ × 3⁶ × 5^a
To make this expression a perfect cube, we need to determine the smallest value of 'a' such that the exponent of 5 is a multiple of 3.
We know that the prime factorization of a perfect cube has exponents that are multiples of 3. Therefore, we need to find the smallest multiple of 3 that is greater than or equal to 6 (the exponent of 3).
The smallest multiple of 3 that is greater than or equal to 6 is 9.
Therefore, if we set 'a' equal to 9, the expression becomes:
2⁹ × 3⁶ × 5⁹
Each exponent in this expression is now a multiple of 3, making it a perfect cube.
Hence, the value of 'a' that would make the expression a perfect cube is 9