B1.2

determine, through investigation using a variety of tools (e.g., calculator, paper and pencil, graphing technology) and strategies (e.g., patterning; finding values from a graph; interpreting the exponent laws), the value of a power with a rational exponent (i.e., $x^{m/n}$, where $x>0$ and $m$ and $n$ are integers) Sample problem: The exponent laws suggest that $4^{1/2}\times 4^{1/2}=4^1$. What value would you assign to $4^{1/2}$? What value would you assign to $27^{1/3}$? Explain your reasoning. Extend your reasoning to make a generalization about the meaning of $x^{1/n}$, where $x>0$ and $n$ is a natural number.