Question

Simplify: (5x^4)^2
(1 point)
Responses

25x6
25 x to the 6th power

5x6
5 x to the 6th power

25x8
25 x to the 8th power

10x8
10 x to the 8th power
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Answer 1

To simplify \((5x^4)^2\), you apply the power of a product rule and the power of a power rule:

1. Apply the power of a product rule:
\[
(ab)^n = a^n b^n
\]
Here, \(a = 5\) and \(b = x^4\), so:
\[
(5x^4)^2 = 5^2 (x^4)^2
\]

2. Calculate \(5^2\):
\[
5^2 = 25
\]

3. Apply the power of a power rule for \(x^4\):
\[
(x^4)^2 = x^{4 \cdot 2} = x^8
\]

Putting it all together:
\[
(5x^4)^2 = 25x^8
\]

So, the simplified expression is \(\boxed{25x^8}\).