Simplify (3k^4)^4

Problem

(3*k^4)^4

Solution

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

2. Distribute the outer exponent of 4 to both the coefficient 3 and the variable term k^4

(3*k^4)^4=3^4⋅(k^4)^4

3. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n) to the variable term.

(k^4)^4=k^(4⋅4)=k^16

4. Evaluate the numerical constant 3^4 by multiplying 3 by itself four times.

3^4=3⋅3⋅3⋅3=81

5. Combine the simplified parts into a single expression.

81⋅k^16=81*k^16

Final Answer

(3*k^4)^4=81*k^16

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