To simplify \( 64^{5/6} \), we can start by breaking it down.
First, we recognize that \( 64 \) can be expressed as a power of \( 2 \):
\[ 64 = 2^6 \]
Now, we can substitute \( 64 \) in the original expression:
\[ 64^{5/6} = (2^6)^{5/6} \]
Using the power of a power property in exponents, we multiply the exponents:
\[ (2^6)^{5/6} = 2^{6 \cdot (5/6)} = 2^5 \]
Now we can simplify \( 2^5 \):
\[ 2^5 = 32 \]
Thus, the simplified form of \( 64^{5/6} \) is:
\[ \boxed{32} \]