Evaluate (0.25)^(-2): Solving Negative Exponent Problems

First, let's convert the decimal fraction in the problem to a simple fraction:

$0.25=\frac{25}{100}=\frac{1}{4}$

where we remembered that 0.25 is 25 hundredths, meaning:

$25\cdot\frac{1}{100}=\frac{25}{100}$

If so, let's write the problem:

$(0.25)^{-2}=\big(\frac{1}{4}\big)^{-2}=\text{?}$

Now we'll use the negative exponent law:

$a^{-n}=\frac{1}{a^n}$

and deal with the fraction expression inside the parentheses:

$\big(\frac{1}{4}\big)^{-2}=(4^{-1})^{-2}$

when we applied the above exponent law to the expression inside the parentheses,

Next, we'll recall the power of a power law:

$(a^m)^n=a^{m\cdot n}$

and we'll apply this law to the expression we got in the last step:

$(4^{-1})^{-2}=4^{(-1)\cdot(-2)}=4^2=16$

where in the first step we carefully applied the above law and used parentheses in the exponent to perform the multiplication between the powers, then we simplified the resulting expression, and finally calculated the numerical result from the last step.

Let's summarize the solution steps:

$(0.25)^{-2}=\big(\frac{1}{4}\big)^{-2}=4^{(-1)\cdot(-2)}=16$

Therefore, the correct answer is answer B.