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Negative Exponents

Simplify: $(2a^{-2}b^{3})^{2}(4a^{3}b^{-1})^{-3}$

$(2a^{-2}b^{3})^{2}(4a^{3}b^{-1})^{-3}$

Remember: $a^{-1}=\frac{1}{a}$

$(\frac{2b^3}{a^2})^{2}(\frac{4a^3}{b})^{-3}$

$(\frac{2b^3}{a^2})^{2}(\frac{1}{(\frac{4a^3}{b})^{3}})$

$(\frac{4b^6}{a^4})(\frac{1}{\frac{64a^9}{b^3}})$ , $(a^{m})^{n}=a^{mn}$

Remember: $\frac{1}{\frac{a}{b}}=\frac{b}{a}$

$(\frac{4b^6}{a^4})(\frac{b^3}{64a^9})$ , $a^{m}\times a^{n}=a^{m+n}$

$\frac{b^{6}b^{3}}{16a^{4}a^{9}}=\frac{b^9}{16a^{13}}$