what is the simplified form of -(-2x to the third power) to the fourth power and why?

Question

anonymous · Answer

Is the (-2x) to the third power or only the x?

anonymous · Answer

$$\large -((-2x)^3)^4 or -(-2x^3)^4 or (-(-2x)^3)^4 or . . . ?$$

anonymous · Answer

the last one, grade 9 multiple choice

anonymous · Answer

sorry the second one

anonymous · Answer

Apply the 4th power to everything in parentheses, then apply the '-' on the outside.

anonymous · Answer

$$\large \rightarrow -((-2)^4 \cdot (x^3)^4)$$

anonymous · Answer

options for answer are 8x to the 12th, or 16x to the 12th, or either one in the negative, 4 options.

anonymous · Answer

so 16x to the 12th

anonymous · Answer

nope, it would be -16x to the 12th , i forgot about the 2nd - sign, right?

radar · Answer

$$-16x ^{12}$$
Provided that the negative sign is outside of the parenthesis.

anonymous · Answer

Yes, don't forget about that little neg' on the outside. Those little minus signs are easy to lose.

anonymous · Answer

thanks for the help, thats one of the many wrongs on my kids test, i didn't know how to do that one.