EX.—Find ^{1.4}√(17) and ^{14}√(17). Set 17 on E to 1·4 on D, and over 1 on D read 7·56 on upper E scale and 1·224 on lower E scale. EX.—Find ^{0·031}√(0·914). Set 0·914 on -E to 3·1 on D, and over 10 on D read 0·055 on upper -E scale. When the exponent _n_ is fractional, it is often possible to obtain the result directly with one setting of the slide. Thus to determine 1·135^{¹⁷⁄₁₆} by the first method we find ¹⁷⁄₁₆ = 1·0625, and placing 1·135 on E to 1 on D, read 1·144 on E over 1·0625 on D. By the direct method we place 1·135 on the E scale on 1·6 on D, and over 1·7 on D read 1·144 on E. It will be seen that since the scale D is assumed to run from 1 to 10 we are unable to read 16 and 17 on this scale; but it is obvious that the _ratios_ (1·7)/(1·6) and (17)/(16) are identical, and it is with the ratio only that we are, in effect, concerned. Since an expression of the form _x_^{-_n_} = (1)/(_x^n_) or ((1)/(_x_))^{_n_}, the required value may be obtained by first determining the reciprocal of _x_ and proceeding as before. By using both the direct and reciprocal log.-log. scales (E and -E) in conjunction however, the required value can be read directly from the rule, and the preliminary calculation entirely avoided. In the Davis form of rule, the result can be read on the -E scale, used in conjunction with the D scale of the rule, _x_ on E being set to the index mark in the aperture in the back of the rule. EX.—Find the value of 1·195^{−1·65}. Set 1·195 on E to the index in the left aperture in the back of the rule, and over 1·65 on D read 0·745 on the -E scale. It may be noted in passing that the log.-log. scale affords a simple means for determining the logarithm or anti-logarithm of a number to any base. For this purpose it is necessary to set the base of the given system on E to 1 on D, when _under_ any number on E will be found its logarithm on D. Thus, for common logs., we set the base 10 on E to 1 on D, and under 100 we find 2, the required log. Similarly we read log. 20 = 1·301; log. 55 = 1·74; log. 550 = 2·74, etc. Reading reversely, over 1·38 on D we find its antilog. 24 on E; also antilog. 1·58 = 38; antilog. 1·19 = 15·5, etc. For logs. of numbers under 10 we set the base 10 to 10 on D; hence the readings on D will be read as one-tenth their apparent value. Thus log. 3 = 0·477; log. 5·25 = 0·72; antilog. 0·415 = 2·6; antilog. 0·525 = 3.·35, etc. The logs. of the numbers on the lower half of the E scale will also be found on the D scale; but a consideration of Fig. 14 will show that this will be read as _one-tenth_ its face value if the base is set to 1 on D, and as _one-hundredth_ if the base is set to 10.