MHB Simplifying expression with exponents

[tmt1]

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)?

 

[Greg]

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?

 

[tmt1]

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 $4^n\cdot (-x)^n$ ?

 

[Greg]

Yes.