Sure, let's evaluate the expression step by step:
Given:
[tex]\[ \left(\frac{1}{8}\right)^{\frac{1}{3}} \][/tex]
Step 1: Understand the expression. The given expression involves a base of [tex]\(\frac{1}{8}\)[/tex] raised to the exponent of [tex]\(\frac{1}{3}\)[/tex].
Step 2: Determine what raising [tex]\(\frac{1}{8}\)[/tex] to the [tex]\(\frac{1}{3}\)[/tex] power means. This means finding the cube root of [tex]\(\frac{1}{8}\)[/tex] because raising a number to the [tex]\( \frac{1}{n} \)[/tex] power is equivalent to taking the [tex]\( n \)[/tex]-th root of that number.
Step 3: Recall that the cube root of a fraction is found by taking the cube root of the numerator and the cube root of the denominator separately:
[tex]\[ \left( \frac{1}{8} \right)^{\frac{1}{3}} = \frac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}} \][/tex]
Step 4: Calculate the cube roots:
[tex]\[ 1^{\frac{1}{3}} = 1 \][/tex]
[tex]\[ 8^{\frac{1}{3}} = 2 \][/tex]
Thus, we get:
[tex]\[ \frac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}} = \frac{1}{2} \][/tex]
Therefore, the value of:
[tex]\[ \left(\frac{1}{8}\right)^{\frac{1}{3}} = \frac{1}{2} \][/tex]
So, the final result is:
[tex]\[ 0.5 \][/tex]
