Simplifying expression with exponents

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Discussion Overview

The discussion revolves around the simplification of expressions involving exponents, specifically focusing on the expression $(-4x^n)$ and its equivalence to other forms. Participants explore the implications of negative signs in mathematical expressions and how they affect the simplification process.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant questions why $(-4x^n)$ is equal to $(-4)^n * x^n$ and not $(-4)^n * (-x)^n$, suggesting that the negative sign applies only to the first term in the expression.
  • Another participant clarifies that $-4x^n$ can be interpreted as $-4 \cdot x^n$, and if the expression were intended as $(-4x)^n$, it would equal $(-4)^n \cdot x^n$ or $4^n \cdot (-x)^n$.
  • There is a reiteration that $-4 \cdot -x$ simplifies to $4x$, not $-4x$.
  • A later reply confirms the equivalence of $(-4)^n \cdot x^n$ and $4^n \cdot (-x)^n$.

Areas of Agreement / Disagreement

Participants appear to agree on the equivalence of the expressions involving exponents, but there is some initial uncertainty regarding the application of the negative sign in the context of the original expression.

Contextual Notes

The discussion does not resolve the broader implications of negative signs in expressions, nor does it clarify all assumptions regarding the interpretation of the expressions involved.

tmt1
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Supposing I have

$$(-4x^n)$$

Why does it equal $(-4)^n * x^n$ and not $(-4)^n * (-x) ^ n$?

When we have a negative symbol it only applies to the first item in an expression? so $-xbcw$ equals $b * c * w * (-x)$? Which means if we wanted the other items to be negative we would have to do $x(-b)(-c)w$ (for $b$ and $c$ to be negative and the other items to be positive)?
 
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Essentially you have $-4x^n$ which is equal to $-4\cdot x^n$.

If you intended $(-4x)^n$ then we have $(-4x)^n=(-4)^n\cdot x^n$ or $4^n\cdot (-x)^n$.

$-4\cdot-x=4x$ not $-4x$.

Does that help?
 
greg1313 said:
Essentially you have $-4x^n$ which is equal to $-4\cdot x^n$.

If you intended $(-4x)^n$ then we have $(-4x)^n=(-4)^n\cdot x^n$ or $4^n\cdot (-x)^n$.

$-4\cdot-x=4x$ not $-4x$.

Does that help?

So, in no uncertain terms, $(-4)^n\cdot x^n$ equals $4^n\cdot (-x)^n$ ?
 
Yes.
 

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