Simplify (4a^3)^2

Problem

(4*a^3)^2

Solution

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

2. Apply the rule to the expression by distributing the exponent 2 to both the coefficient 4 and the variable term a^3

(4)^2⋅(a^3)^2

3. Evaluate the numerical coefficient by squaring 4

4^2=16

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

(a^3)^2=a^(3⋅2)

5. Multiply the exponents to find the final power of a

a^6

6. Combine the simplified coefficient and variable term.

16*a^6

Final Answer

(4*a^3)^2=16*a^6

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