1.	Express the following ratios in their simplest forms: 1. Ratio 0.0900 : 0.180 Correct Answer 3:6 2. Ratio: $$\frac{6}{8} : \frac{10}{7}$$ Correct Answer 21:40 3. Ratio 3 : 15 Correct Answer 1:5

2.	Write the following as percentages 1. Number: 0.47 Correct Answer 47 % 2. Number: $$\frac{7}{5}$$ Correct Answer 140 % 3. Number: 2.0 Correct Answer 200 %

3.	Write the following as a fraction $$ 14.29 \%$$ Correct Answer $$\frac{1}{7}$$

4.	Logs Solve the following for x: $$\ln\left({\left(4x\right)}^{2}\right) + \ln\left({\left(5x\right)}^{2}\right) = \ln\left(x\right) + -3$$ Correct Answer $$ x = {\left(\frac{\exp\left(-3\right)}{400}\right)}^{\frac{1}{3}} $$

5.

Powers 1. Please simplify the following expression: $$ {x}^{1}{x}^{5} $$ Correct Answer $${x}^{6} $$ 2. Please simplify the following expression: $$ {x}^{\frac{-1}{-3}}{x}^{\frac{-1}{-3}} $$ Correct Answer $${\left({x}^{\frac{1}{3}}\right)}^{2} $$ 3. Please simplify the following expression: $$ {\left({x}^{2}\right)}^{5} $$ Correct Answer $$ {x}^{10} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{4}\right)}^{-6}{y}^{-1}}{{y}^{-5}} $$ Correct Answer $$ \frac{{y}^{4}}{{x}^{24}} $$

6.	Express the following ratios in their simplest forms: 1. Ratio 0.0800 : 0.120 Correct Answer 2:3 2. Ratio: $$\frac{8}{7} : \frac{6}{5}$$ Correct Answer 20:21 3. Ratio 0.150 : 0.210 Correct Answer 5:7

7.	Write the following as percentages 1. Number: 0.66 Correct Answer 66 % 2. Number: $$\frac{2}{3}$$ Correct Answer 66.7 % 3. Number: 2.0 Correct Answer 200 %

8.	Write the following as a fraction $$ 14.29 \%$$ Correct Answer $$\frac{1}{7}$$

9.	Logs Solve the following for x: $$2\ln\left(-6x\right) + \ln\left(3x\right) = \ln\left(x\right) + 5$$ Correct Answer $$ x = {\left(\frac{\exp\left(5\right)}{108}\right)}^{\frac{1}{2}} $$

10.

Powers 1. Please simplify the following expression: $$ {x}^{4}{x}^{-6} $$ Correct Answer $$\frac{1}{{x}^{2}} $$ 2. Please simplify the following expression: $$ {x}^{\frac{-3}{-2}}{x}^{\frac{5}{-2}} $$ Correct Answer $${x}^{\frac{3}{2}}{x}^{\frac{-5}{2}} $$ 3. Please simplify the following expression: $$ {\left({x}^{-1}\right)}^{-5} $$ Correct Answer $$ {x}^{5} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{-4}\right)}^{-2}{y}^{6}}{{y}^{5}} $$ Correct Answer $$ {x}^{8}y $$