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Answer :
Final answer:
The equivalent expression to the fraction (4/5)^6 is 4^6/5^6, where both the numerator and denominator are raised to the power of 6 separately, leading to the correct answer of Option D: 4^6/5^6. Therefore, the correct option is D.
Explanation:
The question asks us to find the equivalent expression to the fraction (4/5)⁶. First, let's clarify what this notation means. The exponent on the fraction indicates that we are multiplying the fraction by itself 6 times. Therefore, we apply the exponent to both the numerator and the denominator separately.
(4/5)⁶ is equivalent to 4⁶ divided by 5⁶. The expression simplifies to 4⁶/5⁶ since we are raising both the numerator and the denominator to the power of 6. We do not multiply the fraction by 6 or change the underlying fraction to improper or mixed numbers if not necessary. Hence, the correct answer is Option D: 4⁶/5⁶.
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