https://file.aiquickdraw.com/mathbot/file/1727037193295m0ndn9ok.jpg

Simplify the expression. Write the answer in exponential notation

The expression in the image is:

\[
\frac{\left( \frac{3}{5} \right) \cdot \left( \frac{3}{5} \right)^{3^7}}{\left( \frac{3}{5} \right)^{2^2}}
\]

Let's go step-by-step to simplify this expression using the laws of exponents.

### Step 1: Multiplying powers of the same base.
\[
\left( \frac{3}{5} \right) \cdot \left( \frac{3}{5} \right)^{3^7} = \left( \frac{3}{5} \right)^{1 + 3^7}
\]
Thus, the numerator becomes:
\[
\left( \frac{3}{5} \right)^{1 + 3^7}
\]

### Step 2: Simplifying the denominator.
\[
\left( \frac{3}{5} \right)^{2^2} = \left( \frac{3}{5} \right)^4
\]

### Step 3: Using the division rule for exponents.
\[
\frac{\left( \frac{3}{5} \right)^{1 + 3^7}}{\left( \frac{3}{5} \right)^4} = \left( \frac{3}{5} \right)^{(1 + 3^7) - 4}
\]

### Step 4: Simplifying the exponent.
The exponent simplifies to \(1 + 3^7 - 4 = 3^7 - 3\).

Thus, the final simplified expression in exponential notation is:
\[
\left( \frac{3}{5} \right)^{3^7 - 3}
\]

Let me know if you need further clarification!

Here are some related questions:
1. How do you simplify expressions with multiple powers?
2. What are the rules of exponents for multiplying and dividing powers?
3. What happens if the exponents in the numerator and denominator are equal?
4. Can this expression be further simplified into a decimal form?
5. How do exponent rules apply when dealing with fractional bases?

**Tip:** Always break down exponent operations using exponent rules before simplifying.

Learn how to simplify an expression with fractional bases like (3/5) using exponent rules. This problem involves multiplying and dividing powers, applying key exponent laws step by step. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation