68:17•24:16•12:24•28:12•13

To simplify the expression \(68:17 \cdot 24:16 \cdot 12:24 \cdot 28:12 \cdot 13\), we can rewrite the colons as fractions:

\[ \frac{68}{17} \cdot \frac{24}{16} \cdot \frac{12}{24} \cdot \frac{28}{12} \cdot 13 \]

Now, let's simplify each fraction one by one:

1. \(\frac{68}{17} = 4\) (since \(68 \div 17 = 4\))
2. \(\frac{24}{16} = \frac{3}{2}\) (since \(24 \div 8 = 3\) and \(16 \div 8 = 2\))
3. \(\frac{12}{24} = \frac{1}{2}\) (since \(12 \div 12 = 1\) and \(24 \div 12 = 2\))
4. \(\frac{28}{12} = \frac{7}{3}\) (since \(28 \div 4 = 7\) and \(12 \div 4 = 3\))

Next, let's combine these simplified fractions and the number 13:

\[ 4 \cdot \frac{3}{2} \cdot \frac{1}{2} \cdot \frac{7}{3} \cdot 13 \]

Now we can multiply these together step by step:

1. Calculate \(4 \cdot \frac{3}{2}\): \[ = 4 \cdot \frac{3}{2} = \frac{12}{2} = 6 \]

2. Now calculate \(6 \cdot \frac{1}{2}\): \[ = \frac{6}{2} = 3 \]

3. Next, calculate \(3 \cdot \frac{7}{3}\): \[ = \frac{3 \cdot 7}{3} = 7 \]

4. Finally, multiply \(7 \cdot 13\): \[ = 91 \]

Thus, the final result of the expression \(68:17 \cdot 24:16 \cdot 12:24 \cdot 28:12 \cdot 13\) is:

\[ \boxed{91} \]