REDUCING THE INDEX

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

Does 4 = 2² ? answer

Therefore 2² can be substituted for 4 in 4^(1/8) and = (2²)^(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√(a²b⁶) = answer

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