Final answer:
The expression 16^(3/2) equals 64. This is evaluated by recognizing that 16 can be represented as 4 squared, so when raised to the 3/2 power, it is equivalent to 4 cubed, which calculates to 64.
Step-by-step explanation:
To comprehend the expression 16^(3/2), let's first break it down. The exponent 3/2 indicates that we need to cube the number 16 and then take the square root of the result, or vice versa, as the order in multiplication and division doesn't affect the final outcome. When we simplify 16^(3/2), we are effectively asking to divide 16 into square factors since 16 is a perfect square (4 x 4), and then multiply 3 of those square factors together.
Breaking it down step by step:
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- Recognize that 16 is 4 squared (4^2).
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- Understand that raising to the power of 3/2 is the same as raising to power 3 and then finding the square root.
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- Perform (4^2)^(3/2) which is the same as 4^(2*(3/2)) = 4^3.
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- Calculate 4 cubed, which is 4 x 4 x 4 = 64.
Thus, 16^(3/2) is equal to 64 because you divide 16 into 4 equal factors (as 16 is 4 squared) and then multiply 3 of those factors (4 x 4 x 4) together.