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Evaluate each expression.$$-\left|7-2^{3}(4-7)\right|$$
$$-31$$
Algebra
Chapter 1
An Introduction to Algebra
Section 7
Exponents and Order of Operations
The Language of Algebra
Equations and Inequalities
Functions
Linear Functions
Quadratic Functions
Polynomials
Oregon State University
Harvey Mudd College
Idaho State University
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and this problem we're being asked to evaluate to given expression. Well, first thing we're gonna do is I see a couple of grouping symbols. So remember, we always want to start with the innermost grew very simple, Which in this case, is the prophecy, which contains four minus seven. Well, four minus seven is negative. Three, we're gonna have minus the absolute value of seven minus due to the third times. Negative three. So now we still need to evaluate inside the absolute value. Simple. So we're gonna follow order of operations. Well, I see subtraction and exponents multiplication. So we first must take care of the export. We're just two to the third. Well, remember, that means two times two times two, which is equal to eight. So now we're left with minus the absolute value of seven. Minus eight times Negative. Three. So now, inside the absolute value. Simple. We have subtraction. Multiplication. So according to the order of operations, we must do the multiplication next. Well, a times negative three is negative. 24. So we're gonna have some negative. The absolute value of seven minus negative. 24 now within the absolute value. Simple. We have seven minus negative. 24. Well, remember, when we subtract, we need to add the opposite, so we're gonna add the opposite. So in other words, we just have seven plus 24 which is equal to 31. So I'm gonna call to the top here. Threw off with minus the absolute value of 31. Well, now we have to take the absolute value of 31 which is just 31. So we have minus the quantity of 31 and minus. This quantity of 31 is just negative 31. So we found the value to the
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