Sure, let's solve each problem step by step.
### Problem 7:
[tex]\[ \frac{9 \times 10^3}{3 \times 10^9} \][/tex]
1. Simplify the fractions:
[tex]\[ \frac{9}{3} = 3 \][/tex]
2. Simplify the exponents using the rules of exponents:
[tex]\[ \frac{10^3}{10^9} = 10^{3-9} = 10^{-6} \][/tex]
3. Combine the results:
[tex]\[ 3 \times 10^{-6} = 3 \times 10^{-6} \][/tex]
So, the result is:
[tex]\[ 3 \times 10^{-6} \][/tex]
### Problem 8:
[tex]\[ \frac{1 \times 10^{-8}}{4 \times 10^{-3}} \][/tex]
1. Simplify the fractions:
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
2. Simplify the exponents using the rules of exponents:
[tex]\[ \frac{10^{-8}}{10^{-3}} = 10^{-8-(-3)} = 10^{-8+3} = 10^{-5} \][/tex]
3. Combine the results:
[tex]\[ 0.25 \times 10^{-5} = 2.5 \times 10^{-6} \][/tex]
So, the result is:
[tex]\[ 2.5 \times 10^{-6} \][/tex]
### Problem 9:
[tex]\[ \frac{6 \times 10^{-6}}{8 \times 10^{-3}} \][/tex]
1. Simplify the fractions:
[tex]\[ \frac{6}{8} = 0.75 \][/tex]
2. Simplify the exponents using the rules of exponents:
[tex]\[ \frac{10^{-6}}{10^{-3}} = 10^{-6-(-3)} = 10^{-6+3} = 10^{-3} \][/tex]
3. Combine the results:
[tex]\[ 0.75 \times 10^{-3} = 0.00075 \][/tex]
So, the result is:
[tex]\[ 7.5 \times 10^{-4} \][/tex] or [tex]\[ 0.00075 \][/tex]
### Problem 10:
[tex]\[ \frac{1.2 \times 10^{-5}}{3.6 \times 10^{-7}} \][/tex]
1. Simplify the fractions:
[tex]\[ \frac{1.2}{3.6} = 0.3333 \quad (or \frac{1}{3}) \][/tex]
2. Simplify the exponents using the rules of exponents:
[tex]\[ \frac{10^{-5}}{10^{-7}} = 10^{-5-(-7)} = 10^{-5+7} = 10^{2} \][/tex]
3. Combine the results:
[tex]\[ 0.3333 \times 10^{2} = 33.3333 \][/tex]
So, the result is:
[tex]\[ 33.3333 \][/tex]
These are the final results:
1. Problem 7: [tex]\( 3 \times 10^{-6} \)[/tex]
2. Problem 8: [tex]\( 2.5 \times 10^{-6} \)[/tex]
3. Problem 9: [tex]\( 0.00075 \)[/tex]
4. Problem 10: [tex]\( 33.3333 \)[/tex]
