b) $$ \frac{\left(5 a^{-1} b^{2}\right)^{-2}}{125 a^{5} b^{-3}} $$

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Calculate or simplify the expression $$ (5*a^(-1)*b^(2))^(-2)/(125*a^(5)*b^(-3)) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(5a^{-1}b^{2}ight)^{-2}}{\left(125a^{5}b^{-3}ight)}$$
- step1: Remove the parentheses:
  $$\frac{\left(5a^{-1}b^{2}ight)^{-2}}{125a^{5}b^{-3}}$$
- step2: Express with a positive exponent:
  $$\frac{\frac{1}{\left(5a^{-1}b^{2}ight)^{2}}}{125a^{5}b^{-3}}$$
- step3: Rewrite the expression:
  $$\frac{\frac{1}{\left(5a^{-1}b^{2}ight)^{2}}}{\frac{125a^{5}}{b^{3}}}$$
- step4: Multiply by the reciprocal:
  $$\frac{1}{\left(5a^{-1}b^{2}ight)^{2}}	imes \frac{b^{3}}{125a^{5}}$$
- step5: Multiply the terms:
  $$\frac{b^{3}}{\left(5a^{-1}b^{2}ight)^{2}	imes 125a^{5}}$$
- step6: Multiply the terms:
  $$\frac{b^{3}}{3125b^{4}a^{3}}$$
- step7: Reduce the fraction:
  $$\frac{1}{3125ba^{3}}$$
The simplified form of the expression $$ \frac{\left(5 a^{-1} b^{2}ight)^{-2}}{125 a^{5} b^{-3}} $$ is $$ \frac{1}{3125ba^{3}} $$.
The simplified form of the expression is $$ \frac{1}{3125ba^{3}} $$.

b)

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