Answer :
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]
[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]
