I don't understand why x^4=16 instead of -16 when x=-2.?

Question

If x=-2 then why does x^4=16 and not -16? I am confused because when I punch in -2^4 on my calculator it says -16. But if I make the variable = -2 and then say x^4 it gives me the answer 16. Can someone please explain why the answer is 16 and not -16?

Answer 1

Okay, this question seems to be tricky for some people but then if you work it out and present it in a formula, it will work it out easy enough.

Let me show you:



You see that x to the power of 4 =16 so means that the answer should be -2 to the power of 4 meaning multiplying (-2) four times like this:



(-2)*(-2)*(-2)*(-2)



Actually if you work it out, it would get a positive integer, let me break it down step by step



(-2)*(-2)=4 (positive)

4*(-2)=-8 (negative)

-8*(-2)=16 (positive integer)



The main reason that the calculator give you the wrong answer is that you forget to put the bracket sign after the no. (like (-2)^4) so that's why you keep on getting -16 instead of 16 so the calculator thought that the equation you are looking for is -(2^4) so it would turn out as -16 instead of 16.



Hope it helps

Answer 2

(x)^4



=(-2)^4



=(-2)(-2)(-2)(-2)



=16



By the way, anytime you raise a real number (whether neg or pos) to an even power, you'll get a positive answer.



You'll only get a negative answer if you raise a negative real number to an odd power.



By the way, the reason for: "when I punch in -2^4 on my calculator it says -16" is because you didn't use () around the -2. Try it again.

Your way tells the calculator to do 2^4. And then after that, negate it.

Be careful with calculator entry.

Answer 3

-2*-2*-2*-2=16



an even number of negative signs will produce a positive and an odd number of negative signs = a negative



example -2*-2*-2*-2=16 4 negative signs

-2*-2 *-2= -8 3 negative signs makes it a negative



so when you multiply a -8*-2=16 because a negative times a negative= a positive

Answer 4

I find it difficult to accept that "when I punch in -2^4 on my calculator it says -16", mine doesn't, it says error because the function works by taking logarithms, and you can't take the logarithm of a negative number. Anyway, the answer is definitely +16 because four negative signs are equivalent to a positive sign.

Answer 5

x^4 = 16

(-2)^4 = -16



-2*-2*-2*-2

4*4

16



When you do negative two to the power of four, you are multiplying it by itself four times. negative two times negative is 4 and 4 times negative two is negative 8, and negative 8 time negative two is sixteen.

There you go, hope that helps :)

Answer 6

if the power is an even number, you get a plus.

if the power is an odd number, you get a minus



- * - * - * - =+ minus cancellation.

- * - * - = -



edit:

if you type -2^4 in your calculator you'll get (-16), thanks to the list of priorities -> first 2^4, then (-1)*(16)

the right way to type it in the calculator is:

(-2)^4.

Answer 7

because when you multiply a negative number with another negative number you get a positive number. when you multiply a positive number with a negative number you get a negative number.



so here it is step by step

*=multiply

X^4=X*X*X*X

=(-2)*(-2)*(-2)*(-2)

=(-2*-2)*(-2*-2)

=(4)*(4)

=16

Answer 8

are you sure? cause -2^4 IS 16

Answer 9

sure the respond is 2x - 16x^-2. diff x^2 is 2x by making use of the formulation d/dx(x^a) = ax^a-a million. the comparable formulation is used in sixteen/x section. The x interior the denominator will become x^-a million , if it is going to the numerator. Then it somewhat is going to become 16x^-a million. Then by making use of making use of the comparable formulation diff x^a = ax^a-a million. by making use of the sum, a = -a million. then diff we get sixteen(-1x^-a million-a million) = sixteen(-1x^-2) = -16x^-2. as a result the sum is solved.