You need to understand what the exponent is applied to.
[tex] -6^4 [/tex]
means raise 6 to the 4th power, and then take the negative of that. In this case, you apply the exponent only to 6. The negative sign comes later.
[tex] -6^4 = -(6^4) = -(6 \times 6 \times 6 \times 6) = -(1296) = -1296 [/tex]
Now the other case.
[tex] (-6)^4 [/tex]
means the 4th power of the number -6. Now the base is -6, and the exponent is 4. You need to do a multiplication in which you see the base, -6, appearing 4 times as a factor in a multiplication.
[tex] (-6)^4 = (-6) \times (-6) \times (-6) \times (-6) [/tex]
Since there is an even number of negative signs, the answer is positive.
[tex] (-6)^4 = (-6) \times (-6) \times (-6) \times (-6) = 1296 [/tex]
