Simplify (3x^2)^3

Problem

(3*x2)3

Solution

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

2. Apply the rule to the expression by distributing the outer exponent of 3 to both the coefficient 3 and the variable term x2

(3*x2)3=3⋅(x2)3

3. Evaluate the numerical coefficient by calculating 3 which is 3⋅3⋅3=27

3=27

4. Apply the power of a power rule to the variable term, which states that (xa)b=x(a⋅b)

(x2)3=x(2⋅3)

5. Simplify the exponent by multiplying 2 and 3 to get 6

x(2⋅3)=x6

6. Combine the simplified coefficient and the simplified variable term.

27⋅x6=27*x6

Final Answer

(3*x2)3=27*x6

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