a)
16*32*2^4 * 8^3=2^4*2^5*2^4*(2^3)^3=2^{13}*2^9=2^{22}
b)
(5^4)^3*(-5)^4* 125=5^{12}*5^4*5^3=5^{19}
c)
\frac{3^4*(-9)^{12}}{27*243}=\frac{3^4*9^{12}}{3^3*3^5}=\frac{3^{4}*(3^2)^{12}}{3^8}=\frac{3^4*3^{24}}{3^8}=\frac{3^{28}}{3^8}=3^{20}
243|3
81 |3
27 |3
9 | 3
3 | 3
1 |
d)
\frac{1}{27}*(\frac{1}{9})^3*(-\frac{1}{3})^4*\frac{1}{3}=(\frac{1}{3})^3*((\frac{1}{3})^2)^3*(\frac{1}{3})^4*(\frac{1}{3})^1=(\frac{1}{3})^{3+6+4+1}=(\frac{1}{3})^{14}
e)
\frac{81^2*27}{3^5*3*9}=\frac{(3^4)^2*3^3}{3^5*3^1*3^2}=\frac{3^{11}}{3^8}=3^3
81|3
27|3
9 |3
3 |3
1 |