Question

1. Type an equation in the equation editor that uses 2 fractions with parentheses around one of them. Example:
`(2)/(3)` + (-
`(1)/(2)`) =
`(4)/(6) - (3)/(6) = (1)/(6)`

2. Type an expression that has two terms with exponents, and one with a square root. Example:
`2^(3)` +
`9^(2)` +
`√(16)`

3. Type a compound inequality similar to the one below, but with different numbers. It should be set up the same, with all the symbols in the same places.
`((3)/(5) )^(2)` ·
`^(3) √(10) \leq x^(3) - 2x + 5 \leq \sqrt{(1)/(3)`

Answer 1

i)
`(3)/(5) + (- (1)/(2)) = (6)/(10) - (5)/(10) = (1)/(10)`
`\Rightarrow` \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}

ii)
`4^(3) + 8^(2) + √(9)`
`\Rightarrow` 4^{3} + 8^{2} + \sqrt{9}

iii)
`((4)/(5))^(2). \sqrt[3]{8} \leqx^(3) - 3x + 6 \leq \sqrt{(1)/(3)} \Rightarrow \hspace{0.2cm}` (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}

Explanation:

i)
`(3)/(5) + (- (1)/(2)) = (6)/(10) - (5)/(10) = (1)/(10)`
`\Rightarrow` \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}

ii)
`4^(3) + 8^(2) + √(9)`
`\Rightarrow` 4^{3} + 8^{2} + \sqrt{9}

iii)
`((4)/(5))^(2). \sqrt[3]{8} \leqx^(3) - 3x + 6 \leq \sqrt{(1)/(3)} \Rightarrow \hspace{0.2cm}` (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}