EXPONENTS  
Multiplying X's from right to left in the following sequence
[ X X X X X X 1] produces the powers of X iterated to the right.
If Each power of X may be designated a product y,
Then each y is a whole composed of the parts that are each multiplication of X's in the sequence.
 So each exponent of y indicates a multiple or fraction of the sequence of multiplications of X's that produces y.

Enter a number in the upper left textbox to equal X.
 Click an X above or below the division line in the sequence to produce a value for y.
 y is the product of a number of multiplications of X's equal the exponent (n) above the X you clicked.
 Now moving the cursor along the sequence of X's changes the exponent on the y to some part, fraction or multiple of the Xn you clicked.

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After you enter a number for X and click an X in the sequence, click the space button to enter your value for y in the upper right textbox. Press the space bar again to check your answer.
As you move the cursor along the sequence the exponent on Xn and y will change.
 The exponent on y will indicate that the cursor is at a certain fraction or multiple of the position (n) in the sequence you initially clicked.
 Note the numerator of the exponent on y will always equals the exponent on X as you move the cursor
While the denominator of the exponent on y will always equal the exponent on Xn you initially clicked.
 Note when the numerator is equal 1 the value below y is equal the root of y.
 Note when the fraction is negative the value below y is equal the inverse or reciprocal of a fraction or multiple of y.

Arithmetically the denominator of a fractional exponent tells you to first find the (nth) root of  y (the number multiplied (n) times that produces y).
And the numerator of a fractional exponent tell you to what power to raise the (nth) root (the actual number of times you multiply the root).
Enter your value for the nth root (denominator of exponent) of y raised to the given power (numerator of exponent). Click space button to check your answer.