https://file.aiquickdraw.com/mathbot/file/1726447295576fbu0f4bm.jpg

The equation in the image seems to be:

\[
e - 3 \times (-3)^{-3} = (-3)
\]

Let's break this down and solve it step by step:

### Step 1: Simplify the powers
The term \((-3)^{-3}\) can be written as:

\[
(-3)^{-3} = \frac{1}{(-3)^3} = \frac{1}{-27}
\]

### Step 2: Substitute the simplified value
Now, the equation becomes:

\[
e - 3 \times \left( \frac{1}{-27} \right) = -3
\]

### Step 3: Perform the multiplication
The multiplication \(3 \times \frac{1}{-27}\) results in:

\[
3 \times \frac{1}{-27} = \frac{-3}{27} = \frac{-1}{9}
\]

Thus, the equation now is:

\[
e - \frac{1}{9} = -3
\]

### Step 4: Solve for \(e\)
To isolate \(e\), add \(\frac{1}{9}\) to both sides of the equation:

\[
e = -3 + \frac{1}{9}
\]

Convert \(-3\) to a fraction with denominator 9:

\[
e = \frac{-27}{9} + \frac{1}{9} = \frac{-27 + 1}{9} = \frac{-26}{9}
\]

So, the value of \(e\) is:

\[
e = \frac{-26}{9}
\]

Would you like further clarification or additional details on this solution?

Here are some related questions to explore:

1. How do negative exponents affect the value of a term?
2. What happens when multiplying fractions with whole numbers?
3. How can we simplify fractions more efficiently?
4. What are other methods for solving equations involving powers?
5. How do we handle fractional exponents in similar problems?

**Tip**: Always remember that \(x^{-n} = \frac{1}{x^n}\), which is key to solving problems involving negative exponents!

Learn how to solve the equation e - 3 × (-3)⁻³ = (-3) with a step-by-step breakdown. This problem covers negative exponents, powers, and basic algebraic manipulation, making it ideal for students in Grades 8-10.

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