Let's solve the expression step by step:

Given expression:
\[
0.05(1.05)^{10} - 1 + 0.05
\]

### Step 1: Calculate \( (1.05)^{10} \)

\[
(1.05)^{10} = 1.62889463
\]

### Step 2: Multiply by 0.05

\[
0.05 \times 1.62889463 = 0.0814447315
\]

### Step 3: Apply the rest of the expression

\[
0.0814447315 - 1 + 0.05 = 0.0814447315 - 0.95
\]

\[
0.0814447315 - 0.95 = -0.8685552685
\]

So, the final value of the expression is approximately:

\[
-0.8686
\]

Would you like further details or clarifications?

Here are 5 related questions:
1. What happens if you increase the exponent in the expression \( (1.05)^{n} \)?
2. How does changing the base from 1.05 to a larger value affect the final result?
3. What is the effect of removing the subtraction of 1 in the expression?
4. How would the expression change if the 0.05 were inside the exponent instead?
5. How can compound interest be calculated using similar expressions?

**Tip**: When handling exponents in compound growth formulas, small base changes can lead to large final value differences over time.

Learn how to solve the mathematical expression 0.05(1.05)^10 - 1 + 0.05 step by step. This problem involves concepts such as exponents, multiplication, and arithmetic operations. Ideal for students in Grades 9-12, this solution covers exponential growth and how small changes in exponents impact final values.

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