The expression provided in the image is:

$(-3)^4 + (-3)^6 \div (-3)^5 - (-3)^2$

Step-by-Step Solution

1. Evaluate each term separately:

   • $(-3)^4$: Since $4$ is an even power, $(-3)^4 = 81$.
   • $(-3)^6$: Since $6$ is also an even power, $(-3)^6 = 729$.
   • $(-3)^5$: Since $5$ is an odd power, $(-3)^5 = -243$.
   • $(-3)^2$: With an even power, $(-3)^2 = 9$.

2. Perform the division:

   • $\frac{(-3)^6}{(-3)^5} = \frac{729}{-243} = -3$.

3. Substitute values back into the expression:

   $81 + (-3) - 9$

4. Calculate the final result:

   • $81 - 3 = 78$
   • $78 - 9 = 69$

Final Answer

$69$

Would you like further details or have any questions?

Related Questions

1. How would the solution change if $(-3)$ were raised to an odd power in each term?
2. Can you explain why raising a negative number to an even power results in a positive value?
3. How does the order of operations affect expressions with powers and division?
4. What would the result be if all terms used positive 3 instead of $-3$?
5. How can exponents be simplified when using division in expressions?

Tip

When dealing with powers of negative numbers, remember that an even exponent results in a positive outcome, while an odd exponent keeps the result negative.