Simplify (2x^2)^3

Problem

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

(2)^3⋅(x^2)^3

3. Evaluate the numerical constant 2^3

2⋅2⋅2=8

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)=x^6

5. Combine the results to find the simplified expression.

8*x^6

Final Answer

(2*x^2)^3=8*x^6

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