negative exponents and negative numbers

Question

If you have -3 with a -4 exponent

 

Answer 1

Negative exponents have the following property:   n^-m = 1/n^m   OR   1/n^-m = n^m

So for  (-3)^-4 ,  n= -3 and -m= -4 (or m= 4).

Thus,  (-3)^-4 = 1/(-3)⁴. 

Answer 2

(-3)^(-4)

= 1/(-3)^4

= 1/(-3)(-3)(-3)(-3)=1/9 x 1/9

= 1/81

= .01234567901...

1/9 = .111...

1/81 = 1/9x1/9 = .111.../9 = .01234567901...

UNLESS you meant -(3)^(-4) then it = -1/81 = -.01234567901...

Answer 3

Is your question (-3)^-4 ?

Step 1. To express it as a positive exponent, rewrite it as a reciprocal.

Step 2. Now you have ( 1 / -3 )⁴

Step 3. Express it as a quotient of powers. = (1)⁴ / (-3)⁴

step 4. Simplify. = 1/81

Answer 4

-4^-2

Answer 5

We can rewrite (-3^-4) using a positive exponent by taking the reciprocal of the base (-3) and applying the absolute value of the negative exponent (-4) to the denominator of the fraction like this:  1/(-3)⁴.  Now we can simplify the denominator by evaluating (-3)⁴ which is the same as writing (-3)(-3)(-3)(-3) giving us 81.  So our fraction in simplest form is 1/81.  One interesting thing to note here is that raising a negative number by an even numbered exponent gives a positive value (as in our case) and raising a negative number by an odd numbered exponent yields a negative result.