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Which of the following expressions is equivalent to the one shown below? (3/2)8 A 3^8/2^8 B 3^8/2 C 3/2^8 D 8•(3/2)

User Tirth Patel
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1 Answer

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14 votes

Final answer:

The equivalent expression to (3/2)8 is 38 / 28, which is option A. This comes from applying the exponent to both the numerator and the denominator of the fraction independently.

Step-by-step explanation:

The student is tasked with identifying an expression equivalent to (3/2)8. When raising a fraction to an exponent, both the numerator and denominator are raised to that exponent independently. Therefore, the correct equivalent expression is 38 / 28, which corresponds to option A.

To demonstrate this concept using exponents, let's consider an example with smaller numbers: (2/3)2 is equal to 22 / 32 or 4/9 when expanded. Hence, applying this rule to our initial expression, we can confirm that option A is indeed the equivalent expression for (3/2)8.

User Yarning
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