https://file.aiquickdraw.com/mathbot/file/17254070535590l4a3aw5.jpg

The expression in the image is:

\[
\frac{[6^3]^5}{6^{18}}
\]

Let's simplify this step by step:

1. First, simplify the expression \([6^3]^5\). When you raise a power to another power, you multiply the exponents:

\[
[6^3]^5 = 6^{3 \times 5} = 6^{15}
\]

2. Now, substitute this into the original expression:

\[
\frac{6^{15}}{6^{18}}
\]

3. When you divide two expressions with the same base, you subtract the exponents:

\[
6^{15 - 18} = 6^{-3}
\]

4. The final simplified expression is:

\[
6^{-3}
\]

This can also be written as:

\[
\frac{1}{6^3} = \frac{1}{216}
\]

Would you like more details or have any questions about this solution?

---

Here are 5 related questions you might find interesting:

1. How would you simplify the expression \(\frac{[2^4]^3}{2^{10}}\)?
2. What is the value of \(x\) if \(6^x = 1\)?
3. How do you convert a negative exponent to a fraction?
4. What is the result of \(\frac{10^5}{10^2}\)?
5. How do you simplify the expression \(\frac{[7^2]^4}{7^7}\)?

**Tip:** When working with exponents, remember that raising a power to another power involves multiplying the exponents, while dividing like bases involves subtracting the exponents.

Simplify the expression \(\frac{[6^3]^5}{6^{18}}\).

This page provides a step-by-step solution to simplify the expression \(\frac{[6^3]^5}{6^{18}}\), using the Power of a Power Rule and the Quotient of Powers Rule. Learn how to apply these rules to solve exponent problems. Suitable 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