https://file.aiquickdraw.com/mathbot/file/17255980014770p73uccr.jpg

The expression in the image can be written as:

\[
\left( \frac{7^3}{5^2} \right)^4 \times \frac{5^3}{7}
\]

Let's simplify it step by step:

### Step 1: Apply the power to the fraction.
We need to apply the exponent 4 to both the numerator and denominator of the fraction \(\left( \frac{7^3}{5^2} \right)\):

\[
\left( \frac{7^3}{5^2} \right)^4 = \frac{(7^3)^4}{(5^2)^4} = \frac{7^{12}}{5^8}
\]

### Step 2: Multiply the simplified expression by \(\frac{5^3}{7}\).

\[
\frac{7^{12}}{5^8} \times \frac{5^3}{7} = \frac{7^{12} \cdot 5^3}{5^8 \cdot 7}
\]

### Step 3: Simplify the expression by reducing the powers of 7 and 5.

For the powers of 7:
\[
\frac{7^{12}}{7} = 7^{12-1} = 7^{11}
\]

For the powers of 5:
\[
\frac{5^3}{5^8} = 5^{3-8} = 5^{-5}
\]

### Step 4: Final expression.

The simplified expression is:
\[
\frac{7^{11}}{5^5}
\]

This is the most simplified form.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions involving negative exponents?
2. What happens if the powers in the numerator and denominator are the same?
3. How can you apply the distributive property of exponents more efficiently?
4. How do you deal with complex fraction exponents in a more general case?
5. What is the difference between power of a quotient and quotient of powers?

**Tip**: Always simplify exponents step-by-step, especially when working with fractions.

Simplify the expression: (7^3 / 5^2)^4 × (5^3 / 7)

Learn how to simplify the expression (7^3 / 5^2)^4 × (5^3 / 7) using the laws of exponents. Follow the step-by-step solution to apply exponent rules and simplify complex fractional exponents. Ideal for students in Grades 9-11.

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