To solve the expression [tex]\((-3)^3 \div \sqrt{81}-12 \div(-2)^8+\sqrt{25} \cdot 36\)[/tex], let's break it down step by step:
1. Evaluate [tex]\((-3)^3\)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
2. Evaluate [tex]\(\sqrt{81}\)[/tex]:
[tex]\[
\sqrt{81} = 9
\][/tex]
3. Calculate [tex]\((-3)^3 \div \sqrt{81}\)[/tex]:
[tex]\[
\frac{-27}{9} = -3
\][/tex]
4. Evaluate [tex]\((-2)^8\)[/tex]:
Since [tex]\((-2)\)[/tex] raised to an even power results in a positive number,
[tex]\[
(-2)^8 = 256
\][/tex]
5. Calculate [tex]\(12 \div (-2)^8\)[/tex]:
[tex]\[
\frac{12}{256} = 0.046875
\][/tex]
6. Evaluate [tex]\(\sqrt{25}\)[/tex]:
[tex]\[
\sqrt{25} = 5
\][/tex]
7. Calculate [tex]\(\sqrt{25} \cdot 36\)[/tex]:
[tex]\[
5 \times 36 = 180
\][/tex]
8. Combine all parts to get the final result:
[tex]\[
-3 - 0.046875 + 180
\][/tex]
Now, step-by-step:
- Begin with [tex]\(-3\)[/tex],
- Subtract [tex]\(0.046875\)[/tex] from it,
[tex]\[
-3 - 0.046875 = -3.046875
\][/tex]
- Add [tex]\(180\)[/tex] to the result,
[tex]\[
-3.046875 + 180 = 176.953125
\][/tex]
So, the final result of the expression is:
[tex]\[
176.953125
\][/tex]
