Question

Find each of the following products:
$\left(i\right)(-4)\times (-5)\times (-8)\times (-10)$
$\left(ii\right)(-6)\times (-5)\times (-7)\times (-2)\times (-3)$
$\left(iii\right)(-60)\times (-10)\times (-5)\times (-1)$
$\left(iv\right)(-30)\times (-20)\times (-5)$
$\left(v\right)(-3)\times (-3)\times (-3)\times ..6$ times
$\left(vi\right)(-5)\times (-5)\times (-5)\times ...5$ times
$\left(vii\right)(-1)\times (-1)\times (-1)\times ...200$ times
$\left(viii\right)(-1)\times (-1)\times (-1)\times ...171$ times

Answer 1

$\left(i\right)(-4)\times (-5)\times (-8)\times (-10)$

Since the number of negative integers in the product is even, the product will be positive.
$\Rightarrow (-4)\times (-5)\times (-8)\times (-10)=1600$
$\left(ii\right)(-6)\times (-5)\times (-7)\times (-2)\times (-3)$

Since the number of negative integers in the product is odd, the product will be negative.

$\Rightarrow (-6)\times (-5)\times (-7)\times (-2)\times (-3)=-1260$

$\left(iii\right)(-60)\times (-10)\times (-5)\times (-1)$

Since the number of negative integers in the product is even, the product will be positive.

$\Rightarrow (-60)\times (-10)\times (-5)\times (-1)=3000$
$\left(iv\right)(-30)\times (-20)\times (-5)$

Since the number of negative integers in the product is odd, the product will be negative.

$\Rightarrow (-30)\times (-20)\times (-5)=3000$

$\left(v\right)(-3)\times (-3)\times (-3)\times ..6$ times

Since the number of negative integers in the product is even, the product will be positive.
$\Rightarrow (-3)\times (-3)\times (-3)\times ..6$ times $=3^6=729$

$\left(vi\right)(-5)\times (-5)\times (-5)\times ...5$ times

Since the number of negative integers in the product is odd, the product will be negative.

$\Rightarrow (-5)\times (-5)\times (-5)\times ...5$ times $=5^5=-3125$

$\left(vii\right)(-1)\times (-1)\times (-1)\times ...200$ times

Since the number of negative integers in the product is even, the product will be positive.

$\Rightarrow (-1)\times (-1)\times (-1)\times ...200$ times $=(-1{)}^{200}$

$\left(viii\right)(-1)\times (-1)\times (-1)\times ...171$ times

Since the number of negative integers in the product is odd, the product will be negative.
$\Rightarrow (-1)\times (-1)\times (-1)\times ...171$ times $=(-1{)}^{171}=-1$