FMCC Worksheet 3

Worksheet Worksheet 3
A4 US

1.

Calculate $x^{2} \cdot x^{- 5}$ using a presentation that shows all of the individual steps. Then verify that the product rule gives the same result. Give your final answer in the form $x^{n}$ for some number $n .$

2.

Calculate $x^{2 n} \cdot x^{3 n}$ using the product rule. Explain the logic of your result in complete sentences.

3.

Consider the following presentation:

\begin{aligned} x^{3} \cdot x^{- 3} & = x^{3} \cdot \frac{1}{x^{3}} & Definition of negative exponents \\ = \frac{x^{3}}{x^{3}} & Multiply fractions \\ = \frac{x \cdot x \cdot x}{x \cdot x \cdot x} & Definition of exponents \\ = \frac{x \cdot x \cdot x}{x \cdot x \cdot x} & Reduce the fraction \\ = 0 \end{aligned}

Identify and explain the error. What would you suggest as a way for students to avoid this mistake?

Worksheet Worksheet 3 A4US

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Worksheet Worksheet 3
A4 US