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Indices

1. x^-1/4 = 125x^1/2. Answer given 1/625.

2. 8x^-2 = 343x^-1/2. Answer given 4/49.

3. 2x^1/3 = 81/8x^-1. Answer given 27/8.

Solution Preview

Let us move in small steps

1. x^-1/4 = 125x^1/2 :: note that 125 = 5^3, multiply all by x^1/4, and bote that (1/4)+(1/2)=3/4 to obtain
1 = 5^3 x^3/4 :: now divide all by 5^3 to obtain
5^-3 = x^3/4 :: ...

Solution Summary

This provides examples of determining indices for given problems.

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