To find the value of the given expression [tex]\[(-17) \times(-4) \times(-1) \times(-5) - (-15) \times (-3) \times 0 \times (-13) \times (-11),\][/tex] we can break it down into two parts:
1. Calculate the first part:
[tex]\[
(-17) \times (-4) \times (-1) \times (-5)
\][/tex]
- Multiplying two negative numbers results in a positive number:
[tex]\[
(-17) \times (-4) = 68
\][/tex]
- Now, multiplying 68 with [tex]\(-1\)[/tex] results in a negative number:
[tex]\[
68 \times (-1) = -68
\][/tex]
- Finally, multiplying [tex]\(-68\)[/tex] with [tex]\(-5\)[/tex] results in a positive number:
[tex]\[
-68 \times (-5) = 340
\][/tex]
So, the first part of the expression evaluates to 340.
2. Calculate the second part:
[tex]\[
(-15) \times (-3) \times 0 \times (-13) \times (-11)
\][/tex]
- Here, one of the factors is 0. When any number is multiplied by 0, the result is always 0:
[tex]\[
(-15) \times (-3) \times 0 \times (-13) \times (-11) = 0
\][/tex]
So, the second part of the expression evaluates to 0.
3. Combine the results of the two parts:
[tex]\[
340 - 0 = 340
\][/tex]
Therefore, the value of the given expression is [tex]\(\boxed{340}\)[/tex].
