Simplify (2x^2)^3

Problem

(2*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 exponent 3 to both the coefficient 2 and the variable term x2

(2)3⋅(x2)3

3. Evaluate the numerical constant 2

2⋅2⋅2=8

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)=x6

5. Combine the results to find the simplified expression.

8*x6

Final Answer

(2*x2)3=8*x6

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