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 = 10^1/0.3

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

(L ^0.3)^1/0.3 = L^0.3*(1/0.3) = L

Thus, the original equation can be rewritten:

L = 10^1/0.3