Q: What does it mean when you have a fraction as an exponent?
A: Firstly, we must be familiar with the following: Xa/b = b√Xa
When rewriting, think of a fractional exponent as a “tree”. The top number is the number of branches (how many multiples of X there are) and the bottom number is the root.
It is often important to rewrite radicals (√) as fractional exponents. A calculator does not necessarily have the right buttons to type 5√96, but you could instead type in 96/5 to get an answer.
Being able to go back and forth between fractional form and radical form is critical!
Q: Compute (without a calculator): 642/3
A: Rewrite and simplify: 642/3 = 3√642 = (3√64)2 = 42 = 16!