Rewrite the square root as an exponent: (√5)^8 = (51/2)^8.
Apply the power-of-a-power rule (am)n = amn:
(51/2)^8 = 5(1/2)·8 = 54.
Thus the expression simplifies to 54, which equals 625.
Step-by-step simplification of (√5)^8 using exponent rules to get 5^4 = 625. Final answer as a single exponent: 5^4.
Rewrite the square root as an exponent: (√5)^8 = (51/2)^8.
Apply the power-of-a-power rule (am)n = amn:
(51/2)^8 = 5(1/2)·8 = 54.
Thus the expression simplifies to 54, which equals 625.
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