Let's find the product of each given expression step-by-step:
### Expression 1
[tex]\[
\frac{8^3}{8} \times \frac{2}{3} = \frac{6}{14}
\][/tex]
1. Calculate [tex]\(\frac{8^3}{8} \times \frac{2}{3}\)[/tex]:
[tex]\[
(8^3 / 8) \times \frac{2}{3}
\][/tex]
Simplify [tex]\(8^3 / 8\)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
Hence:
[tex]\[
64 \times \frac{2}{3}
\][/tex]
Simplify:
[tex]\[
\frac{128}{3}
\][/tex]
2. Then multiply:
[tex]\[
\frac{128}{3} \times \frac{6}{14}
\][/tex]
Simplify the fractions if possible:
[tex]\[
\frac{128 \times 6}{3 \times 14} = \frac{768}{42} = \frac{128}{7}
\][/tex]
So, the final product is:
[tex]\[
18.285714285714285
\][/tex]
### Expression 2
[tex]\[
\frac{1}{4} \times \frac{3}{9} = \frac{1}{12}
\][/tex]
1. Simply multiply the fractions:
[tex]\[
\frac{1}{4} \times \frac{3}{9}
\][/tex]
2. Simplify each fraction if possible and then multiply:
[tex]\[
\frac{1 \times 3}{4 \times 9} = \frac{3}{36} = \frac{1}{12}
\][/tex]
So, the final product is:
[tex]\[
0.08333333333333333
\][/tex]
### Expression 3
[tex]\[
1 \frac{1}{2} \times 1 \frac{3}{5}
\][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[
1 + \frac{1}{2} = \frac{3}{2}
\][/tex]
[tex]\[
1 + \frac{3}{5} = \frac{8}{5}
\][/tex]
2. Multiply the fractions:
[tex]\[
\frac{3}{2} \times \frac{8}{5} = \frac{24}{10} = 2.4
\][/tex]
So, the final product is:
[tex]\[
2.4000000000000004
\][/tex]
### Expression 4
[tex]\[
3 \times \frac{6}{10} \times \frac{5}{12}
\][/tex]
1. Convert the decimal multiplication:
[tex]\[
3 \times \frac{6}{10} \times \frac{5}{12}
\][/tex]
2. Multiply the given fractions:
[tex]\[
\frac{6}{10} = \frac{3}{5}
\][/tex]
[tex]\[
3 \times \frac{3}{5} \times \frac{5}{12} = 3 \times \frac{3 \times 5}{5 \times 12} = 3 \times \frac{3}{12} = 3 \times \frac{1}{4} = \frac{3}{4} = 0.75
\][/tex]
So, the final product is:
[tex]\[
0.75
\][/tex]
### Expression 5
[tex]\[
2 \frac{1}{7} \times \frac{7}{10}
\][/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[
2 + \frac{1}{7} = \frac{15}{7}
\][/tex]
2. Multiply the fractions:
[tex]\[
\frac{15}{7} \times \frac{7}{10}
\][/tex]
Simplify:
[tex]\[
= \frac{15 \times 7}{7 \times 10} = \frac{15}{10} = 1.5
\][/tex]
So, the final product is:
[tex]\[
1.4999999999999998
\][/tex]
Thus, the results for all the expressions are as follows:
[tex]\[
(18.285714285714285, 0.08333333333333333, 2.4000000000000004, 0.75, 1.4999999999999998)
\][/tex]
