Exercise 45 Page 13

According to the order of operations, expressions inside parentheses are evaluated first, while addition and subtraction are evaluated last. For the given expression, this means evaluating the expression inside the square brackets completely before multiplying it. Notice also that even within this parenthetical expression, we must obey the order of operations. For this, we must remember to evaluate the expression in parentheses first, then evaluate the exponent and multiply these values and at the end subtract and add terms.

Operation	Before Simplification	After Simplification
Add terms	$3[4-8+4^2(2+5)]$	$3[4-8+4^2(7)]$
Calculate power	$3[4-8+4^2(7)]$	$3[4-8+16(7)]$
Multiply	$3[4-8+16(7)]$	$3[4-8+112]$
Add and subtract terms	$3[3-8+112]$	$3[108]$
Multiply	$3[108]$	$324$

The expression equals $324.$