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