Find:
$(i)$ $2^{2/3} \cdot 2^{1/5}$
$(ii)$ $(1/3^3)^7$
$(iii)$ $11^{1/2} / 11^{1/4}$
$(iv)$ $7^{1/2} \cdot 8^{1/2}$

(N/A) $(i)$ Using the law of exponents $a^m \cdot a^n = a^{m+n}$:
$2^{2/3} \cdot 2^{1/5} = 2^{(2/3 + 1/5)} = 2^{(10+3)/15} = 2^{13/15}$
$(ii)$ Using the law of exponents $(a^m)^n = a^{m \cdot n}$:
$(1/3^3)^7 = (3^{-3})^7 = 3^{-3 \cdot 7} = 3^{-21}$
$(iii)$ Using the law of exponents $a^m / a^n = a^{m-n}$:
$11^{1/2} / 11^{1/4} = 11^{(1/2 - 1/4)} = 11^{(2-1)/4} = 11^{1/4}$
$(iv)$ Using the law of exponents $a^m \cdot b^m = (a \cdot b)^m$:
$7^{1/2} \cdot 8^{1/2} = (7 \cdot 8)^{1/2} = 56^{1/2}$