Answer: Understanding Exponents: Inside vs Outside Brackets

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Homework Help Overview

The discussion revolves around the properties of exponents, particularly focusing on the placement of parentheses in expressions involving negative bases. Participants are examining how different arrangements of parentheses affect the outcome of exponentiation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the necessity of parentheses in expressions like (-y^2)^2 and (-y^2)^3, and how these affect the results. There is an exploration of how ambiguity in notation can lead to different interpretations and outcomes.

Discussion Status

Some participants have offered guidance on clarifying the expressions to avoid ambiguity, suggesting the use of additional parentheses. There is an acknowledgment of the need for precision in notation to ensure correct interpretation of the exponent rules.

Contextual Notes

There is a recognition that the original expressions may lead to confusion due to the inherent ambiguity in the notation used for negative bases and exponents. Participants are discussing how to properly format these expressions to reflect the intended calculations.

Styx
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This is probably a very easy question but it is messing me up.

(-y^2)^2 = (-y)^4

but

(-y^2)^3 = (-y^6)

why does one exponent need to be inside the brackets and the other outside?

Example: (-5^2)^2 = 625 = (-5)^4

(-5^2)^3 = -15625 = (-5^6)
 
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You really need to move your parentheses to avoid amibiguity; your first line should really read -(y2)2=-(y4)
 
cristo said:
You really need to move your parentheses to avoid amibiguity; your first line should really read -(y2)2=-(y4)

but that would make the answer -625, not 625
 
Sorry, I read it wrong. Well, in that case, you need more parentheses, since -x^2 is very ambiguous; I would take it to mean -(x^2). You should write ((-y)^2)^2, which is equal to (-y)^4, using the correct exponent rule.
 
Ok, so ((-y)^2)^3 = (-y)^6
 
Last edited:
Yes. Notice that it is also equal to y^6 if you square the inside bracket first, since (-y)^2=y^2
 

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