Questions: Simplify the given exponential expression. (x^-8)^3

Simplify the given exponential expression. (x^-8)^3
Transcript text: Simplify the given exponential expression. \[ \left(x^{-8}\right)^{3} \]
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Solution

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Solution Steps

To simplify the given exponential expression, apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). This means you multiply the exponents together.

Step 1: Apply the Power of a Power Property

To simplify the expression \(\left(x^{-8}\right)^{3}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Here, \(m = -8\) and \(n = 3\).

Step 2: Calculate the New Exponent

Multiply the exponents: \[ -8 \times 3 = -24 \]

Final Answer

The simplified expression is: \[ \boxed{x^{-24}} \]

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