Section 6.3 Deliberate Practice: Exponents
Algebra is a skill, which means it requires practice to become proficient. But it will take more than rote repetition to get there. Deliberate practice is the thoughtful repetition of a task. For each of these sections, you will be given a list of specific skills or ideas to focus on as you practice thinking through the problems.
Focus on these skills:
Write the original expression.
Imagine writing out the various groupings of the variables to reinforce the specific concepts that connect to the formulas.
Pay close attention to the interplay between negative exponents and fractions.
Present your work legibly.
Worksheet Worksheet
Instructions: Simplify the expression, expressing your final answer without fractions.
1.
Simplify \(x^3 \cdot x^6 \cdot x^{-5}\text{.}\)
2.
Simplify \(\left( a^{-4} \right)^3 \cdot a^2\text{.}\)
3.
Simplify \(m^3 \cdot m^2 \cdot m^{-5}\text{.}\)
4.
Simplify \(s^2 \cdot \left( s^3 \right)^{-1}\text{.}\)
5.
Simplify \(y^{-3} \cdot y^6 \cdot y^{-4}\text{.}\)
6.
Simplify \((n^3 \cdot n^2)^{-2} \cdot n^4\text{.}\)
7.
Simplify \(\dfrac{b^3 \cdot b^5}{b^5}\text{.}\)
8.
Simplify \(\dfrac{p^4 \cdot p^3}{\left( p^2 \right)^3}\text{.}\)
9.
Simplify \(\dfrac{v^{-2} \cdot \left( v^3 \right)^2}{v^3 \cdot v^{-1}}\text{.}\)
10.
Simplify \(\dfrac{\left( z^{-3} \right)^{-2} \cdot z^4}{z^2 \cdot \left( z^{-3} \right)^{-2}} \text{.}\)