1.	Express the following ratios in their simplest forms: 1. Ratio 6 : 42 Correct Answer 1:7 2. Ratio: $$\frac{5}{11} : \frac{1}{2}$$ Correct Answer 10:11 3. Ratio 26.4 : 17.6 Correct Answer 3:2

2.	Write the following as percentages 1. Number: 0.0028 Correct Answer 0.28 % 2. Number: $$\frac{3}{4}$$ Correct Answer 75.0 % 3. Number: 1.2 Correct Answer 120 %

3.	Write the following as a fraction $$ 66.67 \%$$ Correct Answer $$\frac{2}{3}$$

4.	Logs Solve the following for x: $$6\ln\left(2x\right) + 4\ln\left(3x\right) = \ln\left(x\right) + -3$$ Correct Answer $$ x = {\left(\frac{\exp\left(-3\right)}{5184}\right)}^{\frac{1}{9}} $$

5.

Powers 1. Please simplify the following expression: $$ {x}^{-2}{x}^{-1} $$ Correct Answer $$\frac{1}{{x}^{3}} $$ 2. Please simplify the following expression: $$ {x}^{\frac{-1}{5}}{x}^{\frac{5}{5}} $$ Correct Answer $${x}^{\frac{-1}{5}}x $$ 3. Please simplify the following expression: $$ {\left({x}^{-5}\right)}^{2} $$ Correct Answer $$ {x}^{-10} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{5}\right)}^{-5}{y}^{4}}{{y}^{-5}} $$ Correct Answer $$ \frac{{y}^{9}}{{x}^{25}} $$

6.	Express the following ratios in their simplest forms: 1. Ratio 19.8 : 46.2 Correct Answer 3:7 2. Ratio: $$\frac{10}{7} : \frac{11}{9}$$ Correct Answer 90:77 3. Ratio 0.140 : 0.0600 Correct Answer 7:3

7.	Write the following as percentages 1. Number: 0.44 Correct Answer 44 % 2. Number: $$\frac{3}{4}$$ Correct Answer 75.0 % 3. Number: 1.7 Correct Answer 170 %

8.	Write the following as a fraction $$ 40.00 \%$$ Correct Answer $$\frac{2}{5}$$

9.	Logs Solve the following for x: $$\ln\left({x}^{-1}\right) + \ln\left({\left(5x\right)}^{-3}\right) = \ln\left(x\right) + 2$$ Correct Answer $$ x = {\left(125\exp\left(2\right)\right)}^{\frac{-1}{5}} $$

10.

Powers 1. Please simplify the following expression: $$ {x}^{-2}{x}^{-3} $$ Correct Answer $$\frac{1}{{x}^{5}} $$ 2. Please simplify the following expression: $$ \frac{{x}^{-6}}{{x}^{5}} $$ Correct Answer $$\frac{1}{{x}^{11}} $$ 3. Please simplify the following expression: $$ {\left({x}^{5}\right)}^{5} $$ Correct Answer $$ {x}^{25} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{6}\right)}^{-1}{y}^{-2}}{{y}^{-4}} $$ Correct Answer $$ \frac{{y}^{2}}{{x}^{6}} $$