Answer :
To simplify the expression \(\left(x^{-4}\right)^{-6}\), we will apply the rules of exponents step by step.
1. Understanding the Base and Exponent:
- The original expression \(\left(x^{-4}\right)^{-6}\) involves a base of \(x^{-4}\) raised to the power of \(-6\).
2. Applying the Power of a Power Rule:
- One of the exponent rules states that \(\left(a^m\right)^n = a^{m \cdot n}\).
Using this rule:
[tex]\[ \left(x^{-4}\right)^{-6} = x^{-4 \cdot -6} \][/tex]
3. Simplifying the Exponent:
- Now, we multiply the exponents:
[tex]\[ -4 \cdot -6 = 24 \][/tex]
Thus:
[tex]\[ \left(x^{-4}\right)^{-6} = x^{24} \][/tex]
Therefore, the simplified form of the expression \(\left(x^{-4}\right)^{-6}\) is \(x^{24}\), which corresponds to choice D.
So, the answer is:
[tex]\[ \boxed{x^{24}} \][/tex]
1. Understanding the Base and Exponent:
- The original expression \(\left(x^{-4}\right)^{-6}\) involves a base of \(x^{-4}\) raised to the power of \(-6\).
2. Applying the Power of a Power Rule:
- One of the exponent rules states that \(\left(a^m\right)^n = a^{m \cdot n}\).
Using this rule:
[tex]\[ \left(x^{-4}\right)^{-6} = x^{-4 \cdot -6} \][/tex]
3. Simplifying the Exponent:
- Now, we multiply the exponents:
[tex]\[ -4 \cdot -6 = 24 \][/tex]
Thus:
[tex]\[ \left(x^{-4}\right)^{-6} = x^{24} \][/tex]
Therefore, the simplified form of the expression \(\left(x^{-4}\right)^{-6}\) is \(x^{24}\), which corresponds to choice D.
So, the answer is:
[tex]\[ \boxed{x^{24}} \][/tex]
