Question

Evaluate expression. $(-7)^{2}$ and $-7^{2}$

   Evaluate expression.
$(-7)^{2}$ and $-7^{2}$

Prealgebra

Alan S. Tussy, R.… 4th Edition

Chapter 2, Problem 69

Instant Answer

Solved by Expert Amy Jiang

07/19/2020

Step 1

In $(-7)^{2}$, the negative sign is included in the parentheses, which means the entire $-7$ is being squared. In $-7^{2}$, only the $7$ is being squared and then the negative sign is applied. Show more…

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Evaluate expression. $(-7)^{2}$ and $-7^{2}$

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Key Concepts

Parentheses Usage with Negative Numbers

Using parentheses in mathematical expressions with negative numbers specifies that the entire enclosed value should be used as the base for the operation. Without parentheses, the negative sign is not included in the exponentiation and is applied after the exponentiation has been performed.

Exponentiation

Exponentiation is the mathematical operation of raising a number to a power. It involves repeated multiplication of the base, and when applied to negative numbers, the presence or absence of parentheses can fundamentally change which part of the expression is being squared.

Order of Operations

The order of operations is a set of rules that determines the sequence in which the operations in an expression are carried out. In expressions with exponents, the exponentiation is performed before applying any negation unless the negative sign is grouped with the base using parentheses.

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