$a)x^8=x^{4\cdot 2}={\left(x^4\right)}^2$

$4^{15}=4^{3\cdot 5}={\left(4^3\right)}^5$

${\left(-\frac{3}{5}\right)}^{10}={\left(-\frac{3}{5}\right)}^{5\cdot 2}={\left[{\left(-\frac{3}{5}\right)}^5\right]}^2$ ${\left(-\frac{3}{5}\right)}^{10}={\left(-\frac{3}{5}\right)}^{5\cdot 2}={\left[{\left(-\frac{3}{5}\right)}^5\right]}^2$

${\left(1,5\right)}^{18}={\left(1,5\right)}^{6\cdot 3}={\left[{\left(1,5\right)}^6\right]}^3$

${\left(-2\right)}^{80}={\left(-2\right)}^{8\cdot 10}={\left[{\left(-2\right)}^8\right]}^{10}$

$b){\left(-3\right)}^5={\left(-3\right)}^{5\cdot 1}={\left[{\left(-3\right)}^5\right]}^1$

$-{\left(-2\right)}^9=-{\left(-1\right)}^9\cdot 2^9=\left(-1\right)\cdot {\left(-1\right)}^9\cdot 2^9={\left(-1\right)}^{10}\cdot 2^9=1\cdot 2^9=2^9=2^{3\cdot 3}={\left(2^3\right)}^3$

$-7^{11}=\left(-1\right)\cdot 7^{11}={\left(-1\right)}^{11}\cdot 7^{11}={\left(-7\right)}^{11}={\left(-7\right)}^{11\cdot 1}={\left({\left(-7\right)}^{11}\right)}^1$

$-{\left(-5\right)}^{20}=-{\left(-5\right)}^{4\cdot 5}=-{\left({\left(-5\right)}^4\right)}^5$