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

Answer 1

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 2

says its wrong

Answer 3

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 4

as a simplified exponent maybe?

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!