Maths Exam

1.	Express the following ratios in their simplest forms: 1. Ratio 55.0 : 38.5 2. Ratio: $$\frac{4}{1} : \frac{7}{9}$$ 3. Ratio 0.180 : 0.600

2.	Write the following as percentages 1. Number: 0.40 2. Number: $$\frac{7}{8}$$ 3. Number: 1.3

3.	Write the following as a fraction $$ 20.00 \%$$

4.	Logs Solve the following for x: $$5\ln\left(-5x\right) + 5\ln\left(-5x\right) = \ln\left(x\right) + 4$$

5.

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

6.	Express the following ratios in their simplest forms: 1. Ratio 7.70 : 38.5 2. Ratio: $$\frac{8}{2} : \frac{8}{6}$$ 3. Ratio 61.6 : 44.0

7.	Write the following as percentages 1. Number: 0.90 2. Number: $$\frac{2}{3}$$ 3. Number: 1.9

8.	Write the following as a fraction $$ 42.86 \%$$

9.	Logs Solve the following for x: $$\ln\left({\left(3x\right)}^{-6}\right) + \ln\left({\left(5x\right)}^{6}\right) = \ln\left(x\right) + 6$$

10.

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