Simplify to a single power of 6:
start fraction, 6, to the power 5 , divided by, 6, cubed, end fraction
6
3

6
5

​

The given expression is:

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

To simplify this, apply the quotient rule for exponents:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Here, \( a = 6 \), \( m = 5 \), and \( n = 3 \). So,

\[
\frac{6^5}{6^3} = 6^{5-3} = 6^2
\]

Thus, the simplified expression is:

\[
6^2 = 36
\]

Would you like more details or have any questions?

---

Here are five related questions to consider:

1. How would you simplify \( \frac{6^7}{6^2} \)?
2. Can you apply the same rule to simplify \( \frac{5^6}{5^4} \)?
3. How do you simplify \( \frac{a^8}{a^3} \) for any base \( a \)?
4. What happens if the exponents are negative, like \( \frac{6^5}{6^{-2}} \)?
5. How do you simplify \( \frac{6^5}{6^5} \)?

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

Simplify to a single power of 6: 6^5 / 6^3

Learn how to simplify the exponential expression 6^5 / 6^3 using the quotient rule for exponents. This step-by-step explanation covers key algebraic concepts, including the subtraction of exponents. 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