Question

Explain why \((–4x)^0 = 1\), but \(–4x^0 = –4\)

Answer 1

I like messing with peoples posts I must admit :)

Answer 2

anything to the 0th power is 1.

Answer 3

all numbers to the power 0 = 1

Answer 4

Because \(-4x^0 = -4(x)^0\)

Answer 5

The zero power is only being applied to the x

Answer 6

second one is -4 times x^0 = -4 * 1 = -4

Answer 7

spose we define an exponent function notated as \(exp_b(x)\)

\[exp_0(-4x)=0\]
\[-4exp_0(x)=-4\]

Answer 8

lol, first one would be the 1 :)

Answer 9

\[(-4x)^0=(-4)^0(x)^0=1\neq-4x^0 = -4(x)^0=4(1)=4\]they are different because of the rule\[(xy)^a=x^ay^a\]in the first case there is distribution of the exponent, in the second there is not

Answer 10

(-4x)^0 - the whole term in the brackets is taken to power 0 so its = 1

Answer 11

(caveat: \(x\neq0\) )

Answer 12

@TuringTest you made a mistake

Answer 13

both explanations are good
however you prefer to see it

Answer 14

right - i was just wondering about x = 0
0^0 is meaningless right?

Answer 15

did I?
let me try to find it

Answer 16

It might be too obvious for you to find.

Answer 17

0^0 is usually regarded as an indeterminate form

Answer 18

dropped the minus :/

Answer 19

Happens to me a lot

Answer 20

I meant:
\[(-4x)^0=(-4)^0(x)^0=1\neq-4x^0 = -4(x)^0=-4(1)=-4\]they are different because of the rule\[(xy)^a=x^ay^a\]in the first case there is distribution of the exponent, in the second there is not
better ? lol
yeah it happens to us all I think, I still hate arithmetic I always say