To simplify \((5x^4)^2\), you apply the power of a product rule and the power of a power rule:
-
Apply the power of a product rule: \[ (ab)^n = a^n b^n \] Here, \(a = 5\) and \(b = x^4\), so: \[ (5x^4)^2 = 5^2 (x^4)^2 \]
-
Calculate \(5^2\): \[ 5^2 = 25 \]
-
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 \(\boxed{25x^8}\).
1 answer