Simplify (2x^2)^-4

Problem

(2*x2)(−4)

Solution

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

(2*x2)(−4)=2(−4)*(x2)(−4)

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

2(−4)*(x2)(−4)=2(−4)*x(−8)

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

2(−4)*x(−8)=1/(2*x8)

4. Evaluate the constant by calculating 2

2=16

5. Combine the results into a single fraction.

1/(16*x8)

Final Answer

(2*x2)(−4)=1/(16*x8)

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