Which of the following is equivalent to [tex](4x^2)^3[/tex]?

A. [tex]64x^8[/tex]
B. [tex]12x^5[/tex]
C. [tex]12x^6[/tex]
D. [tex]4x^5[/tex]
E. [tex]4x^6[/tex]

( 4 x 2 ) 3 = 4 3 ( x 2 ) 3 = 64 x 2 ⋅ 3 = 64 x 6

Answered by Anonymous | 2024-06-24

To solve the expression (4x2)3, we need to apply the rule for raising a power to a power. According to this rule, we multiply the exponents when an exponential expression is raised to another power. The base in your expression is 4x2, and it is raised to the third power.
Here's how you calculate it step-by-step:
Identify the base and the exponent inside the parentheses. In this case, the base is 4x2 and the exponent inside the parentheses is 2.
Apply the power to the base by raising both the numerical coefficient and the variable to the third power: (43)(x2)3.
Multiply the exponents for the variable (x) according to the rule (am)n = am n). This results in x2 3 which simplifies to x6.
Calculate the power of the numerical coefficient: 43 = 4 4 4 = 64.
Combine the numerical coefficient with the variable raised to the correct power to get the simplified result 64x6.
The final answer is 64x6, which corresponds to option A. Thus, the correct answer is A. 64x8.

Answered by IngridBergman | 2024-06-24

The simplified form of \( (4x^2)^3 \) is \( 64x^6 \. None of the provided options match this result. Therefore, the correct answer is not among the choices given.
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Answered by Anonymous | 2024-09-30