3^5/3^0 +2^0+(√(√(3^6 )) )^2-2^4+(1*0-5)^3

Let's simplify the given expression step by step.

The expression is:

\[
\frac{3^5}{3^0} + 2^0 + \left(\sqrt{\sqrt{3^6}}\right)^2 - 2^4 + (1 \times 0 - 5)^3
\]

### 1. First Part: \( \frac{3^5}{3^0} \)
We know that \( 3^0 = 1 \), so the expression simplifies to:
\[
\frac{3^5}{1} = 3^5 = 243
\]

### 2. Second Part: \( 2^0 \)
Any number raised to the power of 0 is 1:
\[
2^0 = 1
\]

### 3. Third Part: \( \left(\sqrt{\sqrt{3^6}}\right)^2 \)
Let's simplify inside the square root first:
\[
3^6 = 729
\]
Then take the square root:
\[
\sqrt{729} = 27
\]
Now take the square root again:
\[
\sqrt{27} \approx 5.196
\]
Finally, square this result:
\[
(5.196)^2 \approx 27
\]

### 4. Fourth Part: \( -2^4 \)
Raise 2 to the power of 4:
\[
2^4 = 16
\]
So this term is:
\[
-16
\]

### 5. Fifth Part: \( (1 \times 0 - 5)^3 \)
First, simplify inside the parentheses:
\[
1 \times 0 = 0
\]
\[
0 - 5 = -5
\]
Now raise this to the power of 3:
\[
(-5)^3 = -125
\]

### Putting It All Together:
Now, add all the parts together:
\[
243 + 1 + 27 - 16 - 125
\]

First, simplify the positive terms:
\[
243 + 1 + 27 = 271
\]

Then subtract the negative terms:
\[
271 - 16 = 255
\]
\[
255 - 125 = 130
\]

### Final Answer:
\[
130
\]

Would you like more details or have any questions?

**Relative Questions:**
1. What would the expression look like if we changed the exponent of 3 in \( 3^6 \) to 7?
2. How does the result change if we alter \( 2^4 \) to \( 2^5 \)?
3. What is the importance of the exponent rules in simplifying \( \frac{3^5}{3^0} \)?
4. Can you find another expression with similar steps but a different base for the exponents?
5. How would the expression change if the term \( (1 \times 0 - 5)^3 \) were squared instead of cubed?

**Tip:** Remember that the order of operations is crucial—handle exponents and roots before multiplication and addition to simplify expressions correctly.

Explore how to simplify the expression 3^5/3^0 + 2^0 + (√(√(3^6)))^2 - 2^4 + (1*0 - 5)^3 step by step. This problem involves exponents, roots, and the order of operations. Suitable for students in Grades 6-8.

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