Question

Explain why (–4x)⁰ = 1, but –4x⁰ = –4.

Answer 1

use draw box below to write the problem, please. I don't understand a word

Answer 2

I think the asker is asking this:\[(-4x)^0=1\]\[-4x^0=-4\]

Answer 3

@Bea_26 -- am I right?

Answer 4

Yep

Answer 5

ok, are you aware that \[a^0=1\]

Answer 6

Yep

Answer 7

for any \(a\) (apart from zero which has some controversy)

Answer 8

ok, good, so can you see that:\[(-4x)^0=(a)^0=a^0=1\]if we let \(a=-4x\)

Answer 9

order of operations

Answer 10

@Bea_26 -- Have you heard of PEMDAS

Answer 11

@asnaseer Yes I Have.

Answer 12

that is what @pgpilot326 is trying to explain now

Answer 13

in the second case you have:\[-4x^0\]so you need to perform the Exponent operation first, and then the multiplication to get:\[-4x^0=-4\times x^0=-4\times 1=-4\]

Answer 14

does that make sense?

Answer 15

A Little.

Answer 16

which part is troubling you?

Answer 17

we know that any number raised to the power of zero is one.
but the exponent only assume the value right below it
so -4x^0 actually means -4* x^0
but when you use parenthesis such as in the case of (-4x)^0
you have to treat -4x as a single value since -4x must be evaluated before evaluating the power.
in other words (-4x)^0 = -4^0 * x^0 = 1* 1 = 1

Answer 18

@asnaseer , The Last Part.