Simplify (2x^2)^-4

Problem

(2*x^2)^(−4)

Solution

1. Apply the power of a product rule, which states that (a*b)^n=a^n*b^n

(2*x^2)^(−4)=2^(−4)*(x^2)^(−4)

2. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n)

2^(−4)*(x^2)^(−4)=2^(−4)*x^(−8)

3. Apply the negative exponent rule, which states that a^(−n)=1/(a^n)

2^(−4)*x^(−8)=1/(2^4*x^8)

4. Evaluate the constant by calculating 2^4

2^4=16

5. Combine the results into a single fraction.

1/(16*x^8)

Final Answer

(2*x^2)^(−4)=1/(16*x^8)

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