Simplify (3x^2)^3

Problem

(3*x^2)^3

Solution

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

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

(3*x^2)^3=3^3⋅(x^2)^3

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

3^3=27

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

(x^2)^3=x^(2⋅3)

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

x^(2⋅3)=x^6

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

27⋅x^6=27*x^6

Final Answer

(3*x^2)^3=27*x^6

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