Sure! Let's solve the expression step-by-step:
[tex]\[
\frac{2}{3} - \frac{5}{7} \times \frac{10}{3} + \sqrt{\frac{343}{49}} \cdot \frac{4}{9} + 4^3
\][/tex]
### Step 1: Calculate the first term
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
### Step 2: Calculate the second term
Multiply the fractions:
[tex]\[
\frac{5}{7} \times \frac{10}{3} = \frac{5 \times 10}{7 \times 3} = \frac{50}{21} \approx 2.380952380952381
\][/tex]
### Step 3: Calculate the third term
First, simplify the fraction under the square root:
[tex]\[
\frac{343}{49} = 7
\][/tex]
Now take the square root of 7:
[tex]\[
\sqrt{7} \approx 2.6457513110645906
\][/tex]
Next, multiply by [tex]\(\frac{4}{9}\)[/tex]:
[tex]\[
2.6457513110645906 \times \frac{4}{9} \approx 1.1758894715842625
\][/tex]
### Step 4: Calculate the fourth term
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
### Step 5: Combine all the terms
[tex]\[
\text{Result} = \frac{2}{3} - \frac{5}{7} \times \frac{10}{3} + \sqrt{\frac{343}{49}} \cdot \frac{4}{9} + 4^3
\][/tex]
[tex]\[
= 0.6666666666666666 - 2.380952380952381 + 1.1758894715842625 + 64
\][/tex]
[tex]\[
\approx 63.46160375729855
\][/tex]
Thus, the final result of the expression is approximately [tex]\(63.46160375729855\)[/tex].
