High School

Which of the following is equal to the fraction below? \((\frac{4}{5})^6\)

A. \(\frac{4^6}{5^6}\)

B. \(\frac{24}{30}\)

C. \(\frac{4^6}{5}\)

D. \(6 \cdot (\frac{4}{5})\)

Answer :

Final answer:

The rule (a/b)ⁿ = aⁿ/bⁿ is used to explain that the fraction (4/5)⁶ is equivalent to 4⁶/5⁶, thus option A: 4⁶/5⁶ is correct.

Explanation:

The question is asking us to determine which of the given options is equal to the fraction (4/5)⁶. Raising a fraction to a power means raising both its numerator and denominator to that power. The property (a/b)ⁿ = aⁿ/bⁿ is a rule in mathematics and it is applicable to any real numbers a and b (b ≠ 0) and any integer n.

From this rule, we can say that (4/5)⁶ means (4⁶/5⁶). Applying this rule, we see that option A. 4⁶/5⁶ mirrors our calculation and is therefore the equal fraction to (4/5)⁶.

Learn more about Fraction Power here:

https://brainly.com/question/34731461

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