Verify the Equality: Is (a·c)/(c²b) = a/(c·b) True or False?

Let's examine the problem first:

$\frac{a\cdot c}{c^2\cdot b}\stackrel{?}{= }\frac{a}{c\cdot b}$Note that we can simplify the expression on the left side, this can be done by reducing the fraction, for this, let's recall the definition of exponents:

$\frac{a\cdot c}{\textcolor{red}{c^2}b} =\\ \frac{a\cdot \not{c}}{\textcolor{red}{\not{c}\cdot c}\cdot b}=\\ \boxed{\frac{a}{c\cdot b}}\\$The expression on the right side is also:

$\frac{a}{c\cdot b}$Therefore the expressions on both sides of the equation (assumed - that holds) are indeed equal, meaning:

$\frac{a\cdot c}{c^2b}= \frac{a}{c\cdot b}\stackrel{!}{= }\frac{a}{c\cdot b}$

(In other words, an identity equation holds - which is true for all possible values of the parameters $a,b,c$)

Therefore, the correct answer is answer A.