https://file.aiquickdraw.com/mathbot/file/17301219122570ggam02s.jpg

*Rewrite the expression in the form \[5^n\].*

To simplify \((5^{-8})(5^{-10})\) and rewrite it in the form \(5^n\), we can use the property of exponents:

\[
a^m \cdot a^n = a^{m+n}
\]

In this case, we have:

\[
5^{-8} \cdot 5^{-10} = 5^{(-8) + (-10)}
\]

Simplifying the exponent:

\[
5^{(-8) + (-10)} = 5^{-18}
\]

So, the answer is:

\[
5^{-18}
\]

Would you like further clarification on this process?

Here are five additional related questions to expand your understanding:

1. How would you simplify \((5^{3})(5^{-4})\)?
2. What is the general rule for multiplying two powers with the same base?
3. How would the answer change if the expression was \((5^{-8})(5^{10})\)?
4. How can you express \(\frac{5^{-8}}{5^{-10}}\) in terms of a single power of 5?
5. What happens if you multiply \((5^a)(5^b)\) where \(a\) and \(b\) are any real numbers?

**Tip:** When multiplying powers with the same base, add the exponents. This property is very useful for simplifying expressions quickly.

Rewrite the expression in the form 5^n: (5^(-8))(5^(-10))

Learn how to simplify the expression (5^-8)(5^-10) and rewrite it in the form 5^n using the laws of exponents. This problem covers exponentiation rules, specifically the product of powers property, making it ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation