Answer:
the simplified form is 6.
B is the correct option.
Step-by-step explanation:
We have to simplify the expression
\(6^{1/3}\times36^{1/3}\)
We can rewrite this expression using the rule \(x^{1/n}\times y^{1/n}=(xy)^{1/n}\)
\(6^{1/3}\times36^{1/3}\\\\=(6\times36)^{1/3}\\\\=(216)^{1/3}\)
Now, we can write 216 = 6^3
\((216)^{1/3}\\\\=(6^3)^{1/3}\)
Now, using the exponent rule \((x^a)^b=x^{ab}\)
\((6^3)^{1/3}=6^{3\times\frac{1}{3}}\\\\=6\)
Therefore, the simplified form is 6.
B is the correct option.
