An important part of algebraic evaluation is applying operations in the correct sequence. … — Armed Services Vocational Aptitude Battery (ASVAB)

An important part of algebraic evaluation is applying operations in the correct sequence. Consider the mathematical expression provided below:

-3^2 + 4 \times [15 \div (2 - 5)] - (-6)

What is the final calculated value of this expression?

Answer: -23

-23

Following the strict order of operations, we first resolve the grouping symbols from the inside out to get

-5

for the bracketed term. Next, we evaluate the isolated exponent

-3^2

-9

. Then, we multiply the

4

by our bracketed result of

-5

to get

-20

. Finally, we perform addition and subtraction from left to right:

-9 + (-20) + 6

, which results in

-23

Evaluate innermost parentheses

(2 - 5) = -3

Order of operations dictates solving expressions inside the innermost grouping symbols first.

Evaluate brackets

[15 \div (-3)] = -5

Continue evaluating operations inside the next level of grouping symbols.

Evaluate exponent

-3^2 = -9

Exponents are evaluated before multiplication and division. The negative sign is outside the base, so only the 3 is squared.

Perform multiplication

4 \times (-5) = -20

Multiplication and division are performed from left to right before any addition or subtraction.

Perform addition and subtraction

-9 + (-20) - (-6) = -23

Add and subtract from left to right. Subtracting a negative number is mathematically equivalent to adding a positive number.

Applying the order of operations (PEMDAS) to expressions with nested grouping symbols, exponents, and signed numbers.

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