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Manipulating Fractional Exponents

To simplify expressions involving fractional exponents, it is helpful to remember the following rule about exponents:

(X a)b = X a*b

For example:

(X 2)3 = X 2*3 = X 6

When a fractional exponent appears on a variable on one side of an equation, you can often exploit this property to simplify the equation. For example, suppose you had the equation:

L 0.3 = 10

You could raise each side to the power 1/0.3:

(L 0.3)1/0.3 = 101/0.3

Applying the above property of exponents to simplify the left hand side:

(L 0.3)1/0.3 = L0.3*(1/0.3) = L

Thus, the original equation can be rewritten:

L = 101/0.3

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 11/29/2003