Chapter 5

Problem: Simplify: \(\left(6 n^{3}\right)^{2}\) $$ \text { Incorrect Answer: } \begin{aligned} &\left(6 n^{3}\right)^{2} \\ &=6^{2}\left(n^{3}\right)^{2} \\ &=36 n^{5} \end{aligned} $$

Problem: Simplify: \(\left(3 p^{3}\right)\left(4 p^{3}+p^{2}\right)\) $$ \begin{array}{r} \text { Incorrect Answer: }\left(3 p^{3}\right)\left(4 p^{3}+p^{2}\right) \\ =12 p^{9}+3 p^{6} \end{array} $$

\(K_{a}=\frac{\left(1.34 \times 10^{-3}\right)\left(1.34 \times 10^{-3}\right)}{9.87 \times 10^{-2}}\)

Problem: Simplify: \(\left(7 n^{4}\right)\left(9 n^{6}\right)\) $$ \text { Incorrect Answer: } \begin{aligned} &\left(7 n^{4}\right)\left(9 n^{6}\right) \\ &=63 n^{(4)(6)} \\ &=63 n^{24} \end{aligned} $$ 95\. Problem: Simplify: \(\frac{15 n^{12}}{3 n^{4}}\) $$ \text { Incorrect Answer: } \begin{aligned} & \frac{15 n^{12}}{3 n^{4}} \\ &=5 n^{12+4} \\ &=5 n^{3} \end{aligned} $$

Problem: Simplify: \((5 x-2)(x-3)\) Incorrect Answer: \((5 x-2)(x-3)\) $$ \begin{aligned} &=5 x(x)+5 x(-3)-2 x-2(3) \\ &=5 x^{2}-15 x-2 x-6 \\ &=5 x^{2}-17 x-6 \end{aligned} $$

\(\frac{x^{9}}{x^{5}}\)

\(C=\frac{\left(1.2 \times 10^{-5}\right)\left(1.5 \times 10^{-1}\right)}{1.8 \times 10^{-5}}\)

Problem: Simplify: \(\frac{15 n^{12}}{3 n^{4}}\) $$ \text { Incorrect Answer: } \begin{aligned} & \frac{15 n^{12}}{3 n^{4}} \\ &=5 n^{12+4} \\ &=5 n^{3} \end{aligned} $$

Problem: Simplify: \((2 p-9)\left(3 p^{2}+6 p-5\right)\) Incorrect Answer: $$ \begin{aligned} &(2 p-9)\left(3 p^{2}+6 p-5\right) \\ &=2 p\left(3 p^{2}\right)+2 p(6 p)+2 p(-5)-9\left(3 p^{2}\right)-9(6 p)-9(-5) \\\ &=6 p^{3}+12 p^{2}+10 p-27 p^{2}-54 p+45 \\ &=6 p^{3}-15 p^{2}-44 p+45 \end{aligned} $$

\(\frac{110 x^{9}}{300 x^{5}}\)

\(f=\frac{\left(6.67 \times 10^{-11}\right)\left(3 \times 10^{-1}\right)\left(9 \times 10^{-1}\right)}{\left(4 \times 10^{-1}\right)^{2}}\)

Problem: Simplify: \((4 x-1)(6 x+1)\) $$ \text { Incorrect Answer: } \begin{aligned} &(4 x-1)(6 x+1) \\ &=4 x(6 x)+4 x(1)-1(6 x)-1(1) \\ &=24 x^{2}+4 x-6 x-1 \\ &=24 x^{2}+2 x-1 \end{aligned} $$

\(\frac{x^{5}}{x^{9}}\)

\(P=\frac{3.5 \times 10^{2} \text { joule }}{2.5 \times 10^{-1} \mathrm{~s}}\)

Problem: Simplify: \((3 p)(p+4)(p+2)\) $$ \text { Incorrect Answer: } \begin{aligned} &(3 p)(p+4)(p+2) \\ &=3 p(p+4)+3 p(p+2) \\ &=3 p(p)+3 p(4)+3 p(p)+3 p(2) \\ &=3 p^{2}+12 p+3 p^{2}+6 p \\ &=6 p^{2}+18 p \end{aligned} $$

\(\frac{5 p^{8}}{100 p^{13}}\)

\(R=\frac{1.5 \times 10^{-6} \mathrm{ohm} \cdot \mathrm{m}}{3.6 \times 10^{-7} \mathrm{~m}^{2}}\)

\(P=\left(5.0 \times 10^{-2} \mathrm{~kg}\right)\left(4.4 \times 10^{1} \frac{\mathrm{m}}{\mathrm{s}}\right)\)

Simplify: \(6(3 x-9)-(x-15)\)

Rewriting notes as soon as possible after class is often recommended to improve your memory of what you learned and your understanding. To rewrite notes, copy anything that you cannot read well, and fill in words or steps that you did not have time to write. At the bottom of the notes, write summary sentences such as "The main topic of today's class was ...," "It is important to know that ....," and "The most common mistake made in these kinds of problems is ..." Rewrite your notes from today's class. If you did not take notes, explain why.

\(P=\left(3.0 \times 10^{-2} \mathrm{~kg}\right)\left(5.4 \times 10^{1} \frac{\mathrm{m}}{\mathrm{s}}\right)\)

Simplify: \(-3(2 x-11)-4(5 x-8)\)

Describe how you currently take notes and what your notes look like.

Rewrite \(\frac{18}{3}\) using a \(\div\) sign instead of a fraction bar.

\(P=3.9 \times 10^{3} \frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}-\left(-2.25 \times 10^{4} \frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}\right)\)

\(P=4.3 \times 10^{3} \frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}-\left(-3.6 \times 10^{4} \frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}\right)\)

\(D=\left(\frac{6 \mathrm{~A} . \mathrm{U} .}{1}\right)\left(\frac{1.49 \times 10^{8} \mathrm{~km}}{1 \mathrm{~A} . \mathrm{U} .}\right)\left(\frac{1 \mathrm{mi}}{1.61 \mathrm{~km}}\right)\)

\(D=\left(\frac{6 \text { light-years }}{1}\right)\left(\frac{9.47 \times 10^{12} \mathrm{~km}}{1 \text { light-year }}\right)\left(\frac{1 \mathrm{mi}}{1.61 \mathrm{~km}}\right)\)

Find the number of gallons delivered per day from the wells to Brantley Reservoir, The Seven Rivers well field ... and an additional three private wells can produce about 20,000 gallons of water per minute that is delivered through a 12 -mile pipeline network directly to Brantley Reservoir located about 12 miles north of Carlsbad. (Source: www.currentargus.com, Sept. 10, 2009)

\(K_{a}=\frac{\left(1.34 \times 10^{-3}\right)\left(1.34 \times 10^{-3}\right)}{9.87 \times 10^{-2}}\)

\(C=\frac{\left(1.2 \times 10^{-5}\right)\left(1.5 \times 10^{-1}\right)}{1.8 \times 10^{-5}}\)

Problem: Rewrite \(0.00000079\) in scientific notation. Incorrect Answer: \(7.9 \times 10^{7}\)

Problem: Evaluate \(\left(6.4 \times 10^{5}\right)\left(3 \times 10^{8}\right)\). Write the answer in scientific notation. Incorrect Answer: \(19.2 \times 10^{13}\)

Problem: Evaluate \(\left(2 \times 10^{3}\right)\left(4 \times 10^{5}\right)\). Write the answer in scientific notation. Incorrect Answer: \(8 \times 10^{15}\)

Problem: Evaluate \(\left(9 \times 10^{-5}\right)\left(3 \times 10^{-7}\right)\). Write the answer in scientific notation. $$ \begin{aligned} \text { Incorrect Answer: } &\left(9 \times 10^{-5}\right)\left(3 \times 10^{-7}\right) \\ &=27 \times 10^{-12} \\ &=2.7 \times 10^{-13} \end{aligned} $$

Are \(5 x^{2}\) and \(5 x^{3}\) like terms? Explain.

Simplify: \(8 x-9 x+12 x-15 x\)

Simplify: \(-3 x^{2}-5 x^{2}+x^{2}-7 x^{2}\)