Evaluate (5²+3):2² = 5²+3:2²: Order of Operations Challenge

In order to determine if the given equation is correct, we will simplify each expression on its sides separately,

This will be done while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these,

A. Let's start with the expression on the left side of the given equation:

$(5^2+3):2^2$First, we'll simplify the expression in parentheses by calculating the numerical value of the exponent term and then perform the addition:

$(5^2+3):2^2 =\\ (25+3):2^2 \\ 28:2^2$Next, we'll calculate the numerical value of the divisor which is a term with an exponent (in fact, if we were to write the division as a fraction, this term would be in the denominator), then we'll perform the division:

$28:2^2 =\\ 28:4=\\ 7$We have completed simplifying the expression on the left side of the given equation, let's summarize the simplification steps,

We got that:

$(5^2+3):2^2 =\\ 28:2^2 =\\ 28:4=\\ 7$

B. Let's continue and simplify the expression on the right side of the given equation:

$5^2+3:2^2$Similar to what we did in the previous part, we'll simplify the expression while following the order of operations,

Note that exponents come before multiplication and division which come before addition and subtraction, so we'll start by calculating the numerical value of the exponent term, which is the second term from the left, and calculate the numerical value of the second exponent term in this expression, which is the first term from the left, then we'll perform the division operation, and finally perform the addition:

$5^2+3:2^2 =\\ 25+3:4=\\ 25+\frac{3}{4} =\\ 25\frac{3}{4}$In the final steps, since the result of the division operation isn't a whole number, we expressed its result as a simple fraction, and the addition result as a mixed number,

We have completed simplifying the expression on the right side of the given equation, this simplification was brief, so there's no need to summarize,

Now let's return to the original equation and substitute the results of simplifying the expressions detailed in A and B:

$(5^2+3):2^2=5^2+3:2^2 \\ \downarrow\\ 7=25\frac{3}{4}$Obviously:

$7\neq25\frac{3}{4}$Therefore the given equation is incorrect, meaning we have a false statement,

Thus the correct answer is answer B.