Question

fully simplify (y^5/y^2)^2 x (y^9/y^5)^5 =

Answer 1

says its wrong

Answer 2

as a simplified exponent maybe?

Answer 3

To simplify the expression \((y^5/y^2)^2 \times (y^9/y^5)^5\), we can follow these steps:

1. Simplify each fraction.
2. Apply the power rule (i.e., \((a^m)^n = a^{m \cdot n}\)).
3. Combine the results.

Let's start with each component:

1. Simplify \((y^5/y^2)^2\):
\[
\frac{y^5}{y^2} = y^{5-2} = y^3
\]
Now raise it to the power of 2:
\[
(y^3)^2 = y^{3 \cdot 2} = y^6
\]

2. Simplify \((y^9/y^5)^5\):
\[
\frac{y^9}{y^5} = y^{9-5} = y^4
\]
Now raise it to the power of 5:
\[
(y^4)^5 = y^{4 \cdot 5} = y^{20}
\]

Now combine the results:
\[
y^6 \times y^{20}
\]

Using the product of powers rule \(a^m \cdot a^n = a^{m+n}\), we get:
\[
y^{6+20} = y^{26}
\]

Thus, the fully simplified expression is:
\[
\boxed{y^{26}}
\]

Answer 4

Let's reevaluate the expression step-by-step to ensure the simplification is correct.

Given the expression:
\[
\left(\frac{y^5}{y^2}\right)^2 \times \left(\frac{y^9}{y^5}\right)^5
\]

**Step 1: Simplify each component**

1. **Simplify \(\left(\frac{y^5}{y^2}\right)^2\)**:
\[
\frac{y^5}{y^2} = y^{5-2} = y^3
\]
Then raise it to the power of 2:
\[
(y^3)^2 = y^{3 \cdot 2} = y^6.
\]

2. **Simplify \(\left(\frac{y^9}{y^5}\right)^5\)**:
\[
\frac{y^9}{y^5} = y^{9-5} = y^4
\]
Then raise it to the power of 5:
\[
(y^4)^5 = y^{4 \cdot 5} = y^{20}.
\]

**Step 2: Combine the results**
Now that we have simplified both components, we can combine them:
\[
y^6 \times y^{20}.
\]
Using the product of powers property:
\[
y^{6 + 20} = y^{26}.
\]

Upon reviewing this step-by-step process, the final result does indeed yield:
\[
\boxed{y^{26}}.
\]

If there is any specific indication of an error with this result or if there are additional details about the problem, please provide them; otherwise, the simplification seems accurate based on algebraic rules.

Answer 5

Thank you for your question! It seems you want the result expressed with exponents in a simplified form, but it looks like we've already reached that with \( y^{26} \). However, if you meant to express the result in a different notation, like factoring out or using different bases, let’s explore that.

Based on the simplification we've done, the final result is:

\[
y^{26}
\]

This is already considered a simplified exponent. In most contexts, \( y^{26} \) is itself in the simplest form as a single term.

If you want to express \( y^{26} \) in a different way, here are some options:

- Using radicals: \( \sqrt{y^{52}} \) (since \( \sqrt{y^{52}} = y^{26} \)).
- Factored form: \( y^{26} = (y^2)^{13} \).

If you have a specific format in mind, just let me know, and I'll be happy to help!