Answered

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Simplify the expression below.
[tex]\[ \left(x^{-4}\right)^{-6} \][/tex]

A. \(x^{-24}\)

B. \(x^{-10}\)

C. \(x^{10}\)

D. [tex]\(x^{24}\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression \(\left(x^{-4}\right)^{-6}\), we can apply the exponentiation rule:

[tex]\[ (a^b)^c = a^{b \cdot c} \][/tex]

Here, we have the expression \((x^{-4})^{-6}\).

1. Identify the base (\(x\)) and the exponents (\(-4\) and \(-6\)).
2. Apply the exponentiation rule:

[tex]\[ (x^{-4})^{-6} = x^{(-4) \cdot (-6)} \][/tex]

3. Calculate the product of the exponents:

[tex]\[ (-4) \cdot (-6) = 24 \][/tex]

So the expression simplifies to:

[tex]\[ x^{24} \][/tex]

Therefore, the correct answer is:

D. [tex]\(x^{24}\)[/tex]
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