1.	Express the following ratios in their simplest forms: 1. Ratio 4 : 12 Correct Answer 1:3 2. Ratio: $$\frac{4}{9} : \frac{1}{11}$$ Correct Answer 44:9 3. Ratio 35 : 25 Correct Answer 7:5

2.	Write the following as percentages 1. Number: 0.62 Correct Answer 62 % 2. Number: $$\frac{2}{5}$$ Correct Answer 40.0 % 3. Number: 1.3 Correct Answer 130 %

3.	Write the following as a fraction $$ 50.00 \%$$ Correct Answer $$\frac{1}{2}$$

4.	Logs Solve the following for x: $$-2\ln\left(2x\right) + -6\ln\left(6x\right) = \ln\left(x\right) + 6$$ Correct Answer $$ x = {\left(186624\exp\left(6\right)\right)}^{\frac{-1}{9}} $$

5.

Powers 1. Please simplify the following expression: $$ {x}^{-3}{x}^{-2} $$ Correct Answer $$\frac{1}{{x}^{5}} $$ 2. Please simplify the following expression: $$ {x}^{\frac{-2}{2}}{x}^{\frac{-3}{2}} $$ Correct Answer $$\frac{{x}^{\frac{-3}{2}}}{x} $$ 3. Please simplify the following expression: $$ {\left({x}^{6}\right)}^{4} $$ Correct Answer $$ {x}^{24} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{3}\right)}^{-6}{y}^{-3}}{{y}^{-4}} $$ Correct Answer $$ \frac{y}{{x}^{18}} $$

6.	Express the following ratios in their simplest forms: 1. Ratio 23.1 : 15.4 Correct Answer 3:2 2. Ratio: $$\frac{8}{2} : \frac{2}{12}$$ Correct Answer 24:1 3. Ratio 13.2 : 46.2 Correct Answer 2:7

7.	Write the following as percentages 1. Number: 0.63 Correct Answer 63 % 2. Number: $$\frac{2}{3}$$ Correct Answer 66.7 % 3. Number: 1.6 Correct Answer 160 %

8.	Write the following as a fraction $$ 33.33 \%$$ Correct Answer $$\frac{1}{3}$$

9.	Logs Solve the following for x: $$(-\ln\left(4x\right)) + \ln\left({\left(4x\right)}^{-4}\right) = \ln\left(x\right) + -5$$ Correct Answer $$ x = {\left(1024\exp\left(-5\right)\right)}^{\frac{-1}{6}} $$

10.

Powers 1. Please simplify the following expression: $$ {x}^{-1}{x}^{2} $$ Correct Answer $$x $$ 2. Please simplify the following expression: $$ \frac{{x}^{-1}}{{x}^{6}} $$ Correct Answer $$\frac{1}{{x}^{7}} $$ 3. Please simplify the following expression: $$ {\left({x}^{2}\right)}^{4} $$ Correct Answer $$ {x}^{8} $$ 4. Please simplify the following expression: $$ \frac{{\left({x}^{-5}\right)}^{-6}{y}^{1}}{{y}^{4}} $$ Correct Answer $$ \frac{{x}^{30}}{{y}^{3}} $$