Question

Simplify the expression -6 to the negative fourth. Is the result same as simplufying the expression (-6) to the negative fourth? Explain.

(please explain the question, i need to study quick and im trying to understand this problem b/c it will be on a test tysm.)

Answer 1

You need to understand what the exponent is applied to.

`-6^4`

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.

`-6^4 = -(6^4) = -(6 * 6 * 6 * 6) = -(1296) = -1296`

Now the other case.

`(-6)^4`

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.

`(-6)^4 = (-6) * (-6) * (-6) * (-6)`

Since there is an even number of negative signs, the answer is positive.

`(-6)^4 = (-6) * (-6) * (-6) * (-6) = 1296`