https://file.aiquickdraw.com/mathbot/file/1726056122486rk2a5glr.jpg

Let's simplify the expression given in the image:

\[
\frac{3^{-5} \times 2^{-5} \times 5^4}{5^{-2} \times 6^{-5}}
\]

### Step 1: Simplify the expression by handling the powers of the same base.

#### For the base \(5\):
- In the numerator, you have \(5^4\).
- In the denominator, you have \(5^{-2}\).
- Using the rule \( \frac{a^m}{a^n} = a^{m-n} \), the combined power of \(5\) is:

\[
5^{4 - (-2)} = 5^{4 + 2} = 5^6
\]

#### For the base \(3\):
- You have \(3^{-5}\) in the numerator, and no \(3\) term in the denominator, so it remains \(3^{-5}\).

#### For the base \(2\):
- You have \(2^{-5}\) in the numerator, and no \(2\) term in the denominator, so it remains \(2^{-5}\).

#### For the base \(6\):
- You have \(6^{-5}\) in the denominator, and no \(6\) term in the numerator. When moved to the numerator, it becomes \(6^5\).

### Step 2: Rewrite the expression with simplified powers:
\[
\frac{3^{-5} \times 2^{-5} \times 5^6 \times 6^5}{1}
\]

### Step 3: Final expression
\[
3^{-5} \times 2^{-5} \times 5^6 \times 6^5
\]

This is the simplified form of the given expression.

Would you like any further details or have any questions?

Here are some questions that might interest you:
1. What is the significance of the negative exponent in the expression?
2. How do you simplify expressions with mixed positive and negative exponents?
3. What are the common mistakes when simplifying exponential expressions?
4. How would the expression change if one of the bases had a zero exponent?
5. How does the simplification change if there were more variables involved?

**Tip:** Always check if you can combine like terms when simplifying exponents to reduce the complexity of the expression.

Simplify: \( \frac{3^{-5} \times 2^{-5} \times 5^4}{5^{-2} \times 6^{-5}} \)

Simplify the given exponential expression: 3^-5 x 2^-5 x 5^4 divided by 5^-2 x 6^-5. Learn how to apply the laws of exponents, including combining powers of the same base and using the negative exponent rule.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation