1 Answer

Camomilk · Answer 1 · 2023-05-30T10:55:50+0000

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Step-by-step explanation:

Let's focus on the portion
$\left(-(1)/(2)\right)^3$ for now.

The exponent 3 means we'll have 3 copies of the base multiplied out like so

$\left(-(1)/(2)\right)^3 = \left(-(1)/(2)\right)*\left(-(1)/(2)\right)*\left(-(1)/(2)\right) = -(1)/(8)$

Two of the negatives pair up and cancel out. We're left with a negative sign in the result. Also 2*2*2 = 8, which explains the denominator.

In short,

$\left(-(1)/(2)\right)^3 = -(1)/(8)$

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We're then going to raise that result to the power of -3

So,

$\bigg[ \left(-(1)/(2)\right)^3 \bigg]^(-3) = \left(-(1)/(8)\right)^(-3) \\\\= (-8)^3 \\\\=(-8)*(-8)*(-8) \\\\= -512$

The second step in that section above is possible because of this exponent rule:
a^(-b) = (1)/(a^b)

The negative exponent means "flip the base to make the exponent positive". Think of -8 as -8/1.

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