https://file.aiquickdraw.com/mathbot/file/17254074465837shysxfj.jpg

The problem states:

"One of the boxes produced by the crayon manufacturer contains \(2^3 \times 2^2 \times 2^7\) crayons. How many crayons are in the box?"

Let's solve this:

Given expression:
\[
2^3 \times 2^2 \times 2^7
\]

Using the laws of exponents, when you multiply powers of the same base, you add the exponents:
\[
2^3 \times 2^2 \times 2^7 = 2^{3+2+7} = 2^{12}
\]

Now, calculate \(2^{12}\):
\[
2^{12} = 4096
\]

So, there are 4,096 crayons in the box.

Would you like more details or have any questions? Here are some related questions to consider:

1. What are the laws of exponents, and how are they applied in different scenarios?
2. How would the answer change if the exponents were different?
3. Can you express the product of powers using addition of logarithms instead?
4. What if the base was a number other than 2—how would the calculation differ?
5. How can you calculate powers of numbers efficiently?

**Tip:** Practice combining and simplifying expressions using exponent rules, as this is a fundamental skill in algebra and higher mathematics.

One of the boxes produced by the crayon manufacturer contains 2^3 × 2^2 × 2^7 crayons. How many crayons are in the box?

Solve the problem of determining how many crayons are in the box when given the expression 2^3 × 2^2 × 2^7. This problem introduces the application of the laws of exponents in simplifying and calculating powers of numbers. 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