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

Begin by converting the decimal fraction in the problem to a simple fraction:

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

Remember that 0.25 is 25 hundredths, meaning:

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

Proceed to write the problem:

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

Apply the negative exponent law:

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

and proceed to deal with the fraction expression inside of the parentheses:

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

We applied the above exponent law to the expression inside of the parentheses.

Next, recall the power of a power law:

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

Apply this law to the expression that we obtained in the last step:

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

in the first step we carefully applied the above law and used parentheses in the exponent to perform the multiplication between the powers. We then proceeded to simplify 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.