Indices I

Questions

1. Simplify $\frac{5c}{2} \div \frac{20c^2}{d}$.
2. Simplify $\frac{x}{2y} \div \frac{3x^2y}{4}$.
3. Express as a single fraction in its simplest form: $\frac{15xy}{12} \div \frac{9x^2}{4y}$.
4. Simplify $\frac{18h^3j^3}{5k^3} \div \frac{3h^5k}{10j^2}$.
5. Write as a single fraction in its simplest form: $\frac{5t^2}{v} \div \frac{25t}{v^3}$.
6. Express your answer as a power of 7:
   a. $7^{12}\div 7^3$.
   b. $\frac{1}{49}$.
7. Given that $\frac{1}{81} = 3^k$, find $k$.

Answers

1. $\frac{d}{8c}$.
2. $\frac{2}{3xy^2}$
3. $\frac{5y^2}{9x}$
4. $\frac{12j^5}{h^2k^4}$
5. $\frac{tv^2}{5}$
6. a. $7^9$,
   b. $7^{-2}$.
7. $k=-4$.