3. Self-Test

Answers to the questions are available at the end of the book.

1. Express the following as a power of the indicated bases:
   1. 729 as a power of 3.
   2. 128 as a power of 2.
   3. [latex](9)^{\frac{3}{2}}[/latex] as a power of 3.
   4. [latex](16)^{\frac{3}{4}}[/latex] as a power of 2.
2. Express the following as a single power:
   1. [latex]3^4 \times 3^{(4 + 2)}[/latex]
   2. [latex]10^4 \times 10^{(3 + 2)}[/latex]
3. Simplify using the laws of exponents and then evaluate, rounding to two decimal places, wherever applicable.
   1. [latex]\displaystyle{\frac{2^3 \times (3)^3 \times 3^4}{2^3 \times (2^3)^2 \times 3^5}}[/latex]
   2. [latex]\displaystyle{\frac{2^4 \times (3^2)^4 \times 2^2}{2^5 \times (3^3)^2 \times 2^0}}[/latex]

4. a. [latex](2^2 \times 3^3 \times 5^0)^{-1}[/latex]
   b. [latex](3^2 \times 2^{-2} \times 5)^0[/latex]
5. a. [latex]\displaystyle{\left(\frac{3}{2}\right)^2 \times \frac{3}{8}}[/latex]
   b. [latex]\displaystyle{4 \times \frac{8}{5} \div \frac{4}{3} + \sqrt{4} - 1}[/latex]
6. a. [latex]\displaystyle{\frac{2}{5} \times \sqrt{100} + 2^4 \div \frac{5}{3}}[/latex]
   b. [latex]\displaystyle{\sqrt{36} \times \frac{4}{3} \div \frac{8}{6} - 7 + 2}[/latex]
7. a. [latex]\displaystyle{\left(\frac{2}{3} + \frac{4}{3}\right)^5}[/latex]
   b. [latex]\displaystyle{\left(\frac{9^{\frac{2}{5}}}{9^{\frac{3}{5}}}\right) \times 3^2}[/latex]
8. a. [latex]-5^3(-25)^3[/latex]
   b. [latex]3^{-2} \times 3^3[/latex]
9. a. [latex](-3)^3 - (-1)^3[/latex]
   b. [latex](-2)^5 \times (4 - 5)^3 - (-10)[/latex]
10. a. [latex](-5)^3 - (-4)^3[/latex]
    b. [latex](-4)^5 \div (-2)^6[/latex]