Question

What the difference between integer exponents. and rational exponents

Answer 1

When we have an integer exponent, we can multiply the base number the amount of times equal to the value of the exponent.

For example:

`\begin{gathered} 2^5=2\cdot2\cdot2\cdot2\cdot2 \\ (2\text{ multiplied by itself 5 times)} \end{gathered}`

When we have rational exponents (in the fraction form, for example), the numerator represents the number of times the base number multiplies itself, and the denominator represents the order of the radical used (for example, a denominator of 2 indicates a square root, a denominator of 3 indicates a cubic root, and so on).

For example:

`2^{(4)/(3)}=\sqrt[3]{2^4}`