Whole numbers, negative integers, rationals, irrationals.
| exponent
x | 2x | ex | 3x | 10x
| -3
| 1/8 =.125
| 1/e3 ≈0.04978
| 1/27 =.037
| 1/1000 =0.001
| -2
| 1/4 =.25
| 1/e2 ≈0.1353
| 1/9 =.1
| 1/100 =0.01
| -1
| 1/2 =0.5
| 1/e ≈0.3678
| 1/3 =.3
| 1/10 =0.1
| 0
| 1
| 1
| 1
| 1
| 1/3 =∛
| 21/3=∛2 ≈1.260
| ∛e ≈1.395
| ∛3 ≈1.442
| ∛10 ≈2.154
| 1/2 =√
| 21/2=20.5=√2 ≈1.414
| √e ≈1.648
| √3 ≈1.732
| √10 ≈3.162
| 1
| 2
| e ≈2.71828
| 3
| 10
| 2
| 4
| e2 ≈7.389
| 9
| 100
| 5/2 =2.5
| 22.5 ≈5.656
| e2.5 ≈12.182
| 32.5 ≈15.588
| 102.5 ≈316.22
| e ≈2.71828
| 2e ≈6.581
| ee ≈15.15
| 3e ≈19.81
| 10e ≈522.7
| 3
| 8
| e3 ≈20.085
| 27
| 1000
| π ≈3.141592
| 2π ≈8.82
| eπ ≈23.141
| 3π ≈31.544
| 10π ≈1385.46
| 4
| 16
| e4 ≈54.598
| 81
| 10000
| 5
| 32
| e5 ≈148.41
| 243
| 100000
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b>0 → bx>0
Going down are increasing exponents, so increasing values.
Going across are increasing bases, so increasing values.
Rational exponent:
bn/d = d√(bn) = (d√b)n
Ex. b5/2 = √(b5) = (√b)5
Ex. b5/3 = ∛(b5) = (∛b)5