Question

Please help asap Evaluate the numerical expression open parentheses 2 to the power of 3 close parentheses to the power of one half.

4
cube root of 4
square root of 8
square root of 128

Answer 1

The expression (2^3)^(1/2) simplifies to the square root of 2^3, which results in the square root of 8.

Step-by-step explanation:

To evaluate the numerical expression ((2 to the power of 3) to the power of one-half), we first need to clarify the base and the exponents. The base is 2, and it is raised to the power of 3, which gives us 23 or 2 x 2 x 2, which equals 8. Next, this result (8) is raised to the power of one-half. Taking a number to the power of one-half is equivalent to finding the square root of that number. Therefore, (23)1/2 is the same as the square root of 8.

To find the square root of 8, we could split it into its prime factors, which are 2 x 2 x 2, but the simplest way is to understand that the square root of 8 simplifies to √2 x √4. Since the square root of 4 is 2, the answer becomes 2√2. But for our multiple-choice problem, we can look for the simplest form, which is the 'square root of 8' as one of the options provided.

Answer 2

• C) square root of 8

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Given expression

• Open parentheses 2 to the power of 3 close parentheses to the power of one half.

Convert it to math language and simplify

• 
  `(2^3)^{(1)/(2) =` Expression as described
• 
  `(8)^{(1)/(2) =` Cube of 2 is 8
• 
  `√(8)` Different form of square root

Correct choice is C