Certainly! Let's solve the given equation step-by-step to find which number is missing from the equation:
[tex]\[
6^{\square} = \sqrt[3]{6}
\][/tex]
First, let's understand what [tex]\(\sqrt[3]{6}\)[/tex] means. The notation [tex]\(\sqrt[3]{6}\)[/tex] represents the cube root of 6. Another way to express the cube root of 6 is by using exponents:
[tex]\[
\sqrt[3]{6} = 6^{1/3}
\][/tex]
Therefore, the equation can be rewritten as:
[tex]\[
6^{\square} = 6^{1/3}
\][/tex]
Now, in order for the equation to be true, the exponents on both sides of the equation must be equal, since the bases (which are both 6) are the same. This means:
[tex]\[
\square = \frac{1}{3}
\][/tex]
Thus, the missing number in the equation is:
[tex]\[
\frac{1}{3}
\][/tex]
So the answer is:
[tex]\[
\frac{1}{3}
\][/tex]
