a)
\(a^3 \times a^5 = a^{3+5} = a^8\)
b)
\(a^6\times a^{-4} = a^{6+(-4)} =a^{6-4} = a^2\)
c)
\(2a^2 \times 3ab = 6a^3b\)
d)
\(3a^2b \times 5a^2b = 15a^4b^2\)
e)
\(a^7 \div a^5 = a^{7-5} = a^2\)
f)
\(a^6 \div a^{-4} = a^{6-(-4)} = a^{6+4} = a^{10}\)
g)
\((f^2)^3 = f^6\)
h)
\((3f^3)^2 = 3^2f^{3\times 2} = 9f^6\)
i)
\((5f^{-4})^2 = 5^2 f^{-4\times 2} = 25f^{-8} = \frac{25}{f^8}\)
j)
\(14^0 = 1\)
k)
\(\frac{55e^5f^7}{5ef^2}= 11 e^{5-1} f^{7-2} = 11 e^4f^5\)
l)
\(\frac{27e^4f^6}{3ef^6} =9e^{4-1}f^{6-6} = 9e^3f^0 = 9e^3\)
m)
\(81^{\frac{1}{2}} = \sqrt{81} =9\)
n)
\(64^{\frac{1}{2}} = \sqrt{64} =8\)
