Consider a rational (i.e. "fractional") exponent...what does the denominator of the fractional exponent represent in radical form? What does the numerator of the fractional exponent represent?

Do the normal rules of exponents (i.e. the product, quotient, and power rules) apply to fractional exponents? What are some of the unique challenges presented in using these rules with fractional exponents? Give an example to make your point.

Question

Consider a rational (i.e. "fractional") exponent...what does the denominator of the fractional exponent represent in radical form? What does the numerator of the fractional exponent represent?

Do the normal rules of exponents (i.e. the product, quotient, and  power rules) apply to fractional exponents? What are some of the unique challenges presented in using these rules with fractional exponents? Give an example to make your point.

anonymous · Answer

The numerator os the "fraction" is the power of the base.  The denominator is the root being taken of the base  ex.

$$8^{2/3} = \sqrt[3]{^{8^{2}}}$$

anonymous · Answer

When you say the numerator os the "fraction" what exactly are you refering to. I am really lost here. What about the second half of the question have an thought on that one.

anonymous · Answer

The numerator would be the 2 on the left hand side of the equation I wrote.

2nd question, I would say they apply.

I would say a difficulty would be when working with x and how negative numbers can cause issues.

anonymous · Answer

Thanks for your response however I am still really confused. Can you give me an example of what you are talking about to make your point on the second question with an explaination?