Evaluate the following expressions:

a. 10^8*10^7
b. 10^9*10^-5
c. 10^6/10^3
d. 10^8/10^-4

To evaluate the expressions involving powers of 10, we apply the laws of exponents. Specifically, for multiplication and division:

1. **Multiplication of powers of the same base**:  
   \[ 10^a \times 10^b = 10^{a+b} \]
   
2. **Division of powers of the same base**:  
   \[ \frac{10^a}{10^b} = 10^{a-b} \]

### Now, let's evaluate each expression:

**a.** \( 10^8 \times 10^7 \)  
   Using the multiplication rule:  
   \[ 10^8 \times 10^7 = 10^{8+7} = 10^{15} \]

**b.** \( 10^9 \times 10^{-5} \)  
   Using the multiplication rule:  
   \[ 10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^{4} \]

**c.** \( \frac{10^6}{10^3} \)  
   Using the division rule:  
   \[ \frac{10^6}{10^3} = 10^{6-3} = 10^3 \]

**d.** \( \frac{10^8}{10^{-4}} \)  
   Using the division rule:  
   \[ \frac{10^8}{10^{-4}} = 10^{8 - (-4)} = 10^{8+4} = 10^{12} \]

### Final answers:
- **a.** \( 10^{15} \)
- **b.** \( 10^4 \)
- **c.** \( 10^3 \)
- **d.** \( 10^{12} \)

Do you want details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is \( 10^5 \times 10^{-2} \)?
2. Simplify \( \frac{10^{12}}{10^6} \).
3. How would you simplify \( (10^3)^4 \)?
4. What is \( 10^7 \times 10^3 \times 10^{-4} \)?
5. Evaluate \( \frac{10^9}{10^{-3}} \).

**Tip:** When multiplying or dividing powers with the same base, always add or subtract the exponents!

Learn how to evaluate expressions involving powers of 10 using the laws of exponents. This tutorial covers multiplication and division of powers with the same base. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation