## Simplifying (y^3 x 2^5)^2

In mathematics, simplifying expressions involves reducing them to their most basic form. Let's break down how to simplify the expression **(y^3 x 2^5)^2**.

### Applying the Exponent Rule

The key to simplifying this expression is understanding the rule of exponents that states: **(a^m)^n = a^(m*n)**.

This means that when raising a power to another power, we multiply the exponents.

### Applying the Rule to our Expression

Let's apply this rule to our expression:

**(y^3 x 2^5)^2 = y^(3 2) x 2^(52)**

### Simplifying Further

Now, we can simplify the exponents:

**y^(3 2) x 2^(52) = y^6 x 2^10**

### Final Result

Therefore, the simplified form of (y^3 x 2^5)^2 is **y^6 x 2^10**.

### Additional Notes

While this is the simplified form, we can also further express 2^10 as 1024. So, another way to represent the expression is **1024y^6**.