Section 5.2: Quotient Rule and Zero Exponents Worksheet 5.2
The Quotient Rule: When $m>n$ we have $\frac{x^m}{x^n}=x^{m-n}$
Example: $\frac{x^5}{x^2}$
Example: $\frac{x^{120}}{x^{100}}$
Example: $\frac{10\phi^6t^8}{4\phi^3t^2}$
The Quotient Rule (Continued): When $m \lt n$ we have $\frac{x^m}{x^n}=\frac{1}{x^{n-m}}$
Example: $\frac{x^2}{x^5}$
Example: $\frac{x^{100}}{x^{120}}$
Example: $\frac{10\phi^3t^8}{4\phi^6t^2}$
Putting it All Together: Using Multiple Rules at Once
Example: Simplify the following expressions.
$\left(\frac{s^2}{s^6}\right)^{9}$
$\left(\frac{15\beta^7u^9}{5\beta^2u^4}\right)\left(\frac{16\beta^8u^7}{12\beta^5u^3}\right)$
Zero Exponents: ANYTHING (almost) TO THE ZERO POWER IS 1!
Example: $4^0$
Example: $(x+y)^0$
Example: $\left[\left(\frac{10v^9\alpha^8}{16v^5\alpha^2}\right)\left(\frac{7v^9\alpha^7}{12v^4\alpha^3}\right)\right]^0$
Example: $\left[\left(\frac{10\theta^9p^6}{20\theta^5p^3}\right)\left(\frac{14\theta^7p^7}{18\theta^3p^4}\right)\right]^0+\left[\left(\frac{20r^7\phi^9}{2w^5p^3}\right)\left(\frac{18\phi^9s^6}{10p^3t^2}\right)\right]^0$
A Nice Fun Paper-Wasting Activity
In your groups, grab a piece of paper. Fold it and tear it in half. Count the pieces.
Then lay the pieces on top of one another, and tear those in half. Count the pieces.
Keep doing this and make a table of the number of tears and and pieces like so:
$$
\begin{array}{c|c}
\mbox{# tears} & \mbox{# pieces}\\\hline
& \\
& \\
& \\
& \\
\end{array}
$$
Try to come up with a general expression which predicts the number of pieces after 2 tears, 3 tears, 4 tears, and
ultimately $n$ tears.