https://file.aiquickdraw.com/mathbot/file/172825797507760hkyktf.jpg

The expression you need to simplify is:

\[
5b^0 \cdot 10b^{-1} \cdot 5b^6
\]

Let’s simplify it step by step:

1. **Simplify powers with base \(b\):**
   - \(b^0 = 1\) because any number raised to the power of 0 is 1.
   - \(b^{-1} = \frac{1}{b}\) because a negative exponent represents the reciprocal.
   - \(b^6\) remains as it is.

So, the expression becomes:

\[
5 \cdot 1 \cdot 10 \cdot \frac{1}{b} \cdot 5b^6
\]

2. **Combine constants:**
   \[
   5 \cdot 10 \cdot 5 = 250
   \]
   So now the expression is:

   \[
   250 \cdot \frac{b^6}{b}
   \]

3. **Simplify the powers of \(b\):**
   - Using the rule \(\frac{b^6}{b} = b^{6-1} = b^5\).

So the final simplified expression is:

\[
250b^5
\]

The simplified answer is \(250b^5\).

Would you like more details on this, or do you have any questions?

Here are 5 related questions to explore:
1. What is the general rule for multiplying terms with the same base but different exponents?
2. How do you simplify expressions with negative exponents?
3. What happens when you multiply constants and powers of variables?
4. Why does any base raised to the power of 0 equal 1?
5. How can you divide powers with the same base?

**Tip:** Remember that when multiplying terms with the same base, you can add their exponents!

Simplify. Express your answer using positive exponents: 5b^0 * 10b^-1 * 5b^6

Learn how to simplify the expression 5b^0 * 10b^-1 * 5b^6 by applying the rules of exponents. This problem involves key concepts like negative exponents and multiplication of powers, suitable for Grade 8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation