(0.6)^(-8)(0.5)^(-4)/((0.3)^(-6)(0.12)^(-2)) =

This question can be solved very quickly if you can convert the decimals to their equivalent fractions. This is a skill that will also help you when you deal with questions on percentages. Therefore, try to make a table of common fractions and their percentage counterparts and use the table whenever you are solving a question like the above.

We also need to know some basic rules of exponents to get rid of the negative powers.
\(a^{-n}\) = \(\frac{1}{a^n}\)

0.6 = \(\frac{3}{5}\), 0.3 = \(\frac{3}{10}\), 0.12 = \(\frac{3}{25}\) and 0.5 = ½.

Substituting the above values in place of the decimals and using the exponent rule, the given expression can be rewritten as,

\((\frac{3}{25})^2\) * \((\frac{3}{10})^6\) / \((\frac{3}{5})^8\) * \((\frac{1}{2})^4\) which can be simplified as,

\((\frac{3^2}{5^4}) * (\frac{3^6 }{ 2^6*5^6}) / (\frac{3^8 }{5^8}) * \frac{1 }{ 2^4}\).

Simplifying the above by cancelling the respective powers, the expression simplifies to \(\frac{1 }{ 2^2 * 5^2}\) or \(\frac{1}{100}\).
The correct answer option is B.

Hope that helps!