To evaluate the numerical expression \(\left(2^3\right)^{\frac{1}{2}}\), we'll follow these steps carefully:
1. First, calculate the exponent \(2^3\):
[tex]\[ 2^3 = 2 \times 2 \times 2 = 8 \][/tex]
2. Now we need to evaluate this result raised to the power of \(\frac{1}{2}\):
[tex]\[ \left(2^3\right)^{\frac{1}{2}} = 8^{\frac{1}{2}} \][/tex]
3. Raising a number to the power of \(\frac{1}{2}\) is equivalent to taking the square root of that number:
[tex]\[ 8^{\frac{1}{2}} = \sqrt{8} \][/tex]
4. Therefore, the value of \(\sqrt{8}\) is:
[tex]\[ \sqrt{8} = 2.8284271247461903 \][/tex]
In conclusion, the numerical evaluation of the expression [tex]\(\left(2^3\right)^{\frac{1}{2}}\)[/tex] is [tex]\(\sqrt{8} = 2.8284271247461903\)[/tex].
