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Answer :
Final answer:
In the given equation 64×625=2ᵃ×5ᵇ, by breaking down 64 and 625 to their prime factors, we find that a equals 6 and b equals 4.
Explanation:
In this question, we are tasked to find the values of a and b given that 64×625 = 2ᵃ×5ᵇ. To solve this, let's first break down the numbers on the left side of the equation into their prime factors. 64 and 625 can be written as:
- 64 = 2â¶
- 625 = 5â´
So, the given equation can be rewritten as 2â¶×5â´ = 2ᵃ×5ᵇ. Looking at this, it's apparent that the powers of individual bases (2 and 5) must be equal on both sides of the equation. Therefore, a equals 6 and b equals 4.
Learn more about prime factorization here:
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