Certainly! Let's solve the expression [tex]\( 4 \times \left(56 \div 3^3\right) + 6^2 + 10^2 \times 5 - 4^3 \)[/tex] step by step.
1. Evaluate [tex]\( 3^3 \)[/tex]:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
2. Evaluate [tex]\( 56 \div 27 \)[/tex]:
[tex]\[
56 \div 27 \approx 2.074074074074074
\][/tex]
3. Multiply the result by 4:
[tex]\[
4 \times 2.074074074074074 \approx 8.296296296296296
\][/tex]
4. Evaluate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 6 \times 6 = 36
\][/tex]
5. Evaluate [tex]\( 10^2 \times 5 \)[/tex]:
[tex]\[
10^2 = 100 \quad \text{and} \quad 100 \times 5 = 500
\][/tex]
6. Evaluate [tex]\( 4^3 \)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
7. Combine all parts of the expression:
- First part (step 3 result): [tex]\( 8.296296296296296 \)[/tex]
- Second part (step 4 result): [tex]\( 36 \)[/tex]
- Third part (step 5 result): [tex]\( 500 \)[/tex]
- Subtract the fourth part (step 6 result): [tex]\( 64 \)[/tex]
Putting it all together:
[tex]\[
8.296296296296296 + 36 + 500 - 64
\][/tex]
8. Add and subtract the parts:
[tex]\[
8.296296296296296 + 36 = 44.296296296296296
\][/tex]
[tex]\[
44.2962962962963 + 500 = 544.2962962962963
\][/tex]
[tex]\[
544.2962962962963 - 64 = 480.2962962962963
\][/tex]
Therefore, the final result of the expression [tex]\( 4 \times \left( 56 \div 3^3 \right) + 6^2 + 10^2 \times 5 - 4^3 \)[/tex] is approximately [tex]\( 480.2962962962963 \)[/tex].
