Let's solve the expression step by step:

\[
\frac{8 \cdot 5^{20}}{5^{19}} - 20 \cdot 5^{17}
\]

### Step 1: Simplify the first term
\[
\frac{8 \cdot 5^{20}}{5^{19}} = 8 \cdot 5^{20-19} = 8 \cdot 5^1 = 8 \cdot 5 = 40
\]

### Step 2: Simplify the second term
\[
20 \cdot 5^{17}
\]

This term remains as is for now: \( 20 \cdot 5^{17} \).

### Step 3: Substitute the simplified terms back into the expression
\[
40 - 20 \cdot 5^{17}
\]

We can now factor out the common factor of 20:
\[
40 - 20 \cdot 5^{17} = 20(2 - 5^{17})
\]

So, the simplified form of the expression is:
\[
20(2 - 5^{17})
\]

This is the final simplified expression.

---

Would you like further details on any step or have any questions?

Here are some related questions you could explore:
1. What if the exponents were higher, like \( 5^{25} \)?
2. How would the expression change if the coefficient 20 were different?
3. What happens if the base 5 is replaced with another base?
4. How can you express \( 5^{17} \) in decimal form?
5. How do logarithms apply to this type of problem?

**Tip:** Always check for common factors when simplifying expressions involving exponents.

Learn how to simplify the expression (8*5^20)/5^19 - 20*5^17 using exponent rules and factoring. This step-by-step solution is ideal for students in Grades 9-12, covering core algebraic concepts and exponentiation rules.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation