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0\sqrt{8a^{3}}\times 5^{4}a^{8}
To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.
0\sqrt{8a^{3}}\times 625a^{8}
Calculate 5 to the power of 4 and get 625.
0\sqrt{8a^{3}}a^{8}
Multiply 0 and 625 to get 0.
0
Anything times zero gives zero.