Use the properties of multiplication in \(\mathbb{Z}\) to find:
a) \( -4 \times (-19) \times 25 \)
b) \( 8 \times 77 \times (-125) \)
c) \( (-2) \times (-25) \times (-50) \times 4 \)
a) \( -4 \times (-19) \times 25 \)
\( = (-4 \times 25) \times (-19) \)
\( = (-100) \times (-19) = 1900 \)
b) \( 8 \times 77 \times (-125) \)
\( = (8 \times -125) \times 77 \)
\( = (-1000) \times 77 = -77000 \)
c) \( (-2) \times (-25) \times (-50) \times 4 \)
\( = [(-2) \times (-50)] \times [(-25) \times 4] \)
\( = 100 \times (-100) = -10000 \)
\( = (-4 \times 25) \times (-19) \)
\( = (-100) \times (-19) = 1900 \)
b) \( 8 \times 77 \times (-125) \)
\( = (8 \times -125) \times 77 \)
\( = (-1000) \times 77 = -77000 \)
c) \( (-2) \times (-25) \times (-50) \times 4 \)
\( = [(-2) \times (-50)] \times [(-25) \times 4] \)
\( = 100 \times (-100) = -10000 \)
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