To determine which expressions are equivalent to \( (56)_3 \), we first need to convert the base 3 number \( (56)_3 \) to its decimal (base 10) equivalent.
We can break down \( (56)_3 \) as follows:
\[ 5 \times 3^1 + 6 \times 3^0 \]
Calculating each term:
\[ 5 \times 3^1 = 5 \times 3 = 15 \] \[ 6 \times 3^0 = 6 \times 1 = 6 \]
Now add these two values:
\[ 15 + 6 = 21 \]
Now, we check which of the given expressions are equal to 21.
- 536: \( 536 \neq 21 \)
- 563: \( 563 \neq 21 \)
- 5363: \( 5363 \neq 21 \)
- 125216: \( 125216 \neq 21 \)
- 2564: \( 2564 \neq 21 \)
None of the provided expressions are equivalent to \( (56)_3 \), which is equal to 21.
Thus, none of the expressions (536, 563, 5363, 125216, 2564) are equivalent to \( (56)_3 \).