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What values of 'a' if any, would make the expression 2⁹ × 3⁶ × 5^a a perfect cube?​

User Timday
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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
User Jacky Wang
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