$a)2^3\cdot 2^5\cdot 2^2=2^{3+5+2}=2^{10}$

$b){\left(-1\right)}^7\cdot \left(-1\right)\cdot {\left(-1\right)}^2\cdot {\left(-1\right)}^{15}={\left(-1\right)}^{7+1+2+15}={\left(-1\right)}^{25}$