Questions: Simplify. (-27)^(-5/3)

Simplify. (-27)^(-5/3)
Transcript text: Simplify. \[ (-27)^{-\frac{5}{3}} \] $\square$
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Solution

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Solution Steps

Step 1: Calculate the Cube Root

To find \((-27)^{-\frac{5}{3}}\), we first calculate the cube root of \(-27\): \[ \sqrt[3]{-27} = 1.5 + 2.598i \]

Step 2: Raise to the Power of 5

Next, we raise the cube root result to the power of 5: \[ (1.5 + 2.598i)^5 = 121.5 - 210.444i \]

Step 3: Take the Reciprocal

Since the original exponent was negative, we take the reciprocal of the result: \[ \frac{1}{121.5 - 210.444i} = 0.002057613168724276 + 0.0035638905505532455i \]

Final Answer

\(\boxed{0.002057613168724276 + 0.0035638905505532455i}\)

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