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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1 answer

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 \(\boxed{25x^8}\).