IDNLearn.com provides a platform for sharing and gaining valuable knowledge. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.

What is the value of the expression below?

[tex]\[
\left(8^{1 / 2}\right)^2
\][/tex]

A. 12
B. 16
C. 8
D. 4


Sagot :

To solve the expression [tex]\(\left(8^{1 / 2}\right)^2\)[/tex], we need to understand a few fundamental concepts about exponents.

1. Exponentiation and Roots: The expression [tex]\(8^{1 / 2}\)[/tex] represents the square root of 8. In other words, [tex]\(8^{1 / 2}\)[/tex] is the number which, when squared, gives 8.

2. Simplifying the Expression: When we raise [tex]\(8^{1 / 2}\)[/tex] to the power of 2, we are essentially squaring the square root of 8. Mathematically, this looks like:
[tex]\[ \left(8^{1 / 2}\right)^2 = (8^{1 / 2}) \cdot (8^{1 / 2}) \][/tex]
According to the properties of exponents, [tex]\((a^{m})^{n} = a^{m \cdot n}\)[/tex]. In our case:
[tex]\[ \left(8^{1 / 2}\right)^2 = 8^{(1/2) \cdot 2} \][/tex]

3. Simplification of Exponents: Now, we multiply the exponents:
[tex]\[ (1 / 2) \cdot 2 = 1 \][/tex]
Thus, the expression simplifies to:
[tex]\[ 8^{1} = 8 \][/tex]

The exact value of the expression [tex]\(\left(8^{1 / 2}\right)^2\)[/tex] is [tex]\(8\)[/tex].

Therefore, the correct answer is:
C. 8