When multiplying negative numbers together it is necessary to use parentheses,
such as (-4)(-4)(-4)(-4)(-4)(-4) to avoid confusion.

When raising a negative number to some power it is necessary to use parentheses,
such as (-4)⁶ if you want the negative value raised to the power.

Here's the problem about the parentheses: (-4)6 and -46 are not the same. We know (-4)6 = (-4)(-4)(-4)(-4)(-4)(-4) = 4096. But, -46 = - (4)(4)(4)(4)(4)(4) = -4096 The problem is that since there are no parentheses in -46, it is being viewed as (-1) times 46. Order of operations dictates that the exponent be done before the multiplication. You can think of it as the exponent 6 being STUCK to the 4, but not to the negative sign. In (-4)6, the exponent 6 is STUCK to the parentheses, and since the parentheses are done first, the 4 gets negated before the exponent is applied.

More Information: The problem we just encountered appeared because the exponent was an even power. If the exponent were an odd power, we could arrive at a correct answer. But, as shown below, -4³ is raising 4 to the third power, and then negating the result. It is not truly raising (-4) to the third power, like (-4)³ is doing.

(-4)³ = (-4)(-4)(-4) = -64
-4³ = -(4)(4)(4) = -64

Since it is usually the intent in these situations to "raise the negative base to the exponent power", avoid confusion and use parentheses!!

More about exponents being EVEN or ODD:

Even powers of negative numbers allow for the negative values to be arranged in pairs. This pairing guarantees that the answer will always be positive. Remember, a negative number times another negative number yields a positive result.

(-3)⁶ = (-3)(-3) • (-3)(-3) • (-3)(-3)
= 9 • 9 • 9
= 729 (positive)

Odd powers of negative numbers, however, always leave one factor of the negative number not paired. This one lone negative term guarantees that the answer will always be negative.

(-3)⁵ = (-3)(-3) • (-3)(-3) • (-3) ← lone factor
= 9 • 9 • (-3)
= -81 (negative)

If a negative base is enclosed in parentheses:   • the result is positive if the exponent is even.   • the result is negative if the exponent is odd. If a negative base is not enclosed in parentheses:   • the result is always negative.

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