To solve the expression [tex]\(8^{\frac{1}{3}}\)[/tex], let's first rewrite it as a radical expression.
The expression [tex]\(8^{\frac{1}{3}}\)[/tex] can be written as the cube root of 8:
[tex]\[ 8^{\frac{1}{3}} = \sqrt[3]{8} \][/tex]
Next, let's evaluate the cube root of 8. We are looking for a number which, when raised to the power of 3, gives us 8. This can be expressed as:
[tex]\[ x^3 = 8 \][/tex]
We know that:
[tex]\[ 2^3 = 2 \times 2 \times 2 = 8 \][/tex]
So:
[tex]\[ \sqrt[3]{8} = 2 \][/tex]
Therefore, the evaluation of the radical expression gives us:
[tex]\[ 8^{\frac{1}{3}} = 2.0 \][/tex]
Thus, [tex]\( 8^{\frac{1}{3}} = 2.0 \)[/tex].
