**REDUCING THE INDEX**

#
Radicals can be written with fractional exponents.^{8}√4 = 4^{(1/8)}

Does 4 = 2^{2} ? answer

Therefore 2^{2} can be substituted for 4 in 4^{(1/8)} and = (2^{2})^{(1/8)}

Next we multiply the exponents resulting in 2^{(2/8)}

This can be reduced to 2^{(1/4)} and rewritten as a radical ^{4}√2

Thus the index has been reduced and ^{8}√4 = ^{4}√2

Try the following examples:

^{8}√16 = answer

^{10}√(a^{2}b^{6}) = answer

return