Question

Evaluate:
(i) $(-6)\times (-15)\times (-5)$

(ii) $(-8)\times (-5)\times 9$

(iii) $9\times (-12)\times 10$

(iv) $(-75)\times 8$

(v) $(-5)\times (-5)\times (-5)\dots \dots$taken $5$ times

(vi) $(-1)\times (-1)\times (-1)\dots \dots$taken $25$ times

Answer 1

$(-1{)}^{oddno.}=-1\&(-1{)}^{evenno.}=1$

(i) $(-6)\times (-15)\times (-5)=(-6\times -15)\times (-5)=\left(90\right)\times (-5)=-450$

(ii) $(-8)\times (-5)\times 9=(-8\times -5)\times 9=\left(40\right)\times \left(9\right)=360$

(iii) $9\times (-12)\times 10=(9\times -12)\times 10=(-108)\times \left(10\right)=-1080$

(iv) $(-75)\times 8=-600$

(v) $(-5)\times (-5)\times (-5)\times (-5)\times (-5)=(-5\times -5)\times (-5\times -5)\times (-5)=25\times 25\times (-5)=-3125$

Other method to do above question.

$(-5{)}^5=(-1\times 5{)}^5=(-1{)}^5\times (5{)}^5=-1\times 30125=-3125$

(vi) $(-1)\times (-1)\times (-1)\dots \dots 25$ times $=(-1{)}^{25}=-1$