3^(5/2)-3^(3/2)
2(3^(3/2)) is the correct expression for 3^(5/2) - 3^(3/2).
To simplify the expression 3^(5/2) - 3^(3/2), we can factor out the common term 3^(3/2), leading to the result of 2(3^(3/2)). This demonstrates that the difference can be expressed in terms of a multiple of the common factor.
This choice represents a numerical constant and does not reflect the relationship between the two terms in the expression. The value of 1 does not arise from simplifying or factoring the original expression, as the calculations yield a different result.
While 2 is a factor in the correct answer, it does not encompass the entire expression. The subtraction of the two terms involves the factor of 3^(3/2), which is necessary to accurately represent the simplification.
This choice suggests a single number rather than a product of terms. The original expression involves exponents and requires factoring out a common base, making 3 an insufficient representation of the final result.
The expression 3^2 equals 9, which does not correlate with the result of the subtraction of the original terms. The simplification does not yield a single power of 3, but rather a product that includes both a coefficient and an exponent term.
The expression 3^(5/2) - 3^(3/2) simplifies to 2(3^(3/2)), demonstrating the importance of factoring in algebraic expressions. The correct choice encapsulates the relationship between the terms, while all other options fail to accurately represent the result of the original expression. Understanding how to factor and simplify is crucial in algebraic manipulations.
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