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To evaluate the expression \( 17 - \left(\frac{5n}{4}\right) + 8^3 \) when \( n = 8 \), we follow these steps:
1. Substitute \( n = 8 \) into the expression:
\[
17 - \left(\frac{5 \cdot 8}{4}\right) + 8^3
\]
2. Simplify inside the parentheses and exponent:
\[
17 - \left(\frac{40}{4}\right) + 8^3
\]
\[
17 - 10 + 8^3
\]
3. Calculate the exponent \( 8^3 \):
\[
8^3 = 512
\]
4. Substitute back into the expression:
\[
17 - 10 + 512
\]
5. Perform the addition and subtraction in the order from left to right:
\[
17 - 10 = 7
\]
\[
7 + 512 = 519
\]
So, the value of the expression \( 17 - \left(\frac{5n}{4}\right) + 8^3 \) when \( n = 8 \) is \( 519 \).