how would I solve a sum like (-3x^2) ( -4x)^(-2)
#negative exponents
final sentinel
fast onyxBOT
how would I solve a sum like (-3x^2) ( -4x)^(-2)
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lament hill
how would I solve a sum like (-3x^2) ( -4x)^(-2)
That's a product, not a sum.
final sentinel
but how do I solve it
lament hill
Okay, so you know the rule $a^b * a^c = a^{b + c}$?
reef mapleBOT
Techie Literate
final sentinel
yes
lament hill
So let's look at what happens when $c = -b$; $a^b * a^{-b} = a^{b + -b} = a^{b - b} = a^0 = 1$
reef mapleBOT
Techie Literate
lament hill
So $a^b * a^{-b} = 1$, which means $a^{-b} = \frac{1}{a^b}$ by simple algebra.
final sentinel
yeah
reef mapleBOT
Techie Literate
lament hill
how would I solve a sum like (-3x^2) ( -4x)^(-2)
(-4x)^(-2) equals what, according to what we just worked out?
final sentinel
and the negative
lament hill
and the negative
...the whole of -4x is our a in this context.
final sentinel
so the answer would be -16x ?
lament hill
Or actually, that's just another exponent property; $(a * b)^c = a^c * b^c$
reef mapleBOT
Techie Literate
lament hill
so the answer would be -16x ?
No.
final sentinel
._.
final sentinel
we add the exponents
lament hill
...no.
final sentinel
._.
lament hill
$(-4x)^{-2} = \frac{1}{(-4x)^2}$
reef mapleBOT
Techie Literate
final sentinel
oh
lament hill
That's what I proved to you.
final sentinel
now I understand
lament hill
Now, $-4x = -1 * 4 * x$, right?
reef mapleBOT
Techie Literate
