High School

Simplify the following expression: (4x^4)^2. Select the correct answer below:
1. 6x^6
2. 4x^8
3. 8x^8
4. 16x^8
5. 4x^6

Answer :

To simplify the expression [tex](4x^4)^2[/tex], we need to apply the power of a power property. This property states that when you raise a power to another power, you multiply the exponents.

Here's a step-by-step explanation:

  1. Start with the expression [tex](4x^4)^2[/tex].

  2. According to the power of a power property, [tex](a^m)^n = a^{m \times n}[/tex]. Therefore, for [tex](4x^4)^2[/tex], you'll do the following:

    • The base '4' is raised to the power of 2.
    • The base 'x^4' is also raised to the power of 2.
  3. Calculate each base separately:

    • The 4 raised to the power of 2 is: [tex]4^2 = 16[/tex].
    • For the variable part, multiply the exponents: [tex](x^4)^2 = x^{4 \times 2} = x^8[/tex].
  4. Combine the results: [tex]16x^8[/tex].

Therefore, the simplified expression is [tex]16x^8[/tex].

Based on the given options, the correct answer is:

4. 16x^8