Simplify: (5x^4)^2

Question

Responses:

5x^6

25x^6

25x^8

10x^8

Answer 1

To simplify \((5x^4)^2\), you apply the power to both the coefficient and the variable:

1. Square the coefficient: \(5^2 = 25\).
2. Square the variable \(x^4\): \((x^4)^2 = x^{4 \cdot 2} = x^8\).

Putting it all together:

\[ (5x^4)^2 = 25x^8 \]

So, the correct response is 25x^8.