6b
[tex]\bold{42a^{3}b^{3} \div 7a^{3}b^{2}}\\\\=42a^{3}b^{3} \div 7a^{3}b^{2}\\\\=(42 \div 7) \times (a^{3}b^{3} \div a^{3}b^{2})\\\\=6 \times (a^{3}b^{3} \div a^{3}b^{2})[/tex]
Apply the Exponent Rule.
" [tex]\bold{x^{x} \div x^{y} = x^{x-y}}[/tex] "
[tex]\bold{6 \times (a^{3}b^{3} \div a^{3}b^{2})}\\\\= 6 \times (a^{3-3}b^{3-2})\\\\= 6 \times (a^{0}b^{1})\\\\= 6 \times (b)\\\\=6b\\\\\boxed{=6b}[/tex]
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