Which number is missing from this equation?

[tex]\[ 6^{\square} = \sqrt[3]{6} \][/tex]

A. [tex]\(\frac{1}{6}\)[/tex]
B. [tex]\(\frac{1}{3}\)[/tex]
C. 2
D. 3



Answer :

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]