Question
Use the power of a power property to simplify: \( (2y^{5})^{2} \)
Ask by Gordon Knight. in South Africa
Dec 28,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 4y^{10} \)
Solution
To simplify \( (2y^{5})^{2} \) using the **power of a power property**, follow these steps:
1. **Understand the Power of a Power Property:**
\[
(a^m)^n = a^{m \times n}
\]
This means you multiply the exponents when raising a power to another power.
2. **Apply the Property to Each Factor:**
\[
(2y^{5})^{2} = 2^{2} \times (y^{5})^{2}
\]
3. **Simplify Each Part:**
- \( 2^{2} = 4 \)
- \( (y^{5})^{2} = y^{10} \) (since \( 5 \times 2 = 10 \))
4. **Combine the Simplified Parts:**
\[
4 \times y^{10} = 4y^{10}
\]
**Final Answer:**
\[
4y^{10}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To simplify \( (2y^{5})^{2} \), you apply the power of a power property, which states that \((a^{m})^{n} = a^{m \cdot n}\). In this expression, the base is \(2y^{5}\). When you square it, you square both the coefficient and the variable: \[ (2y^{5})^{2} = 2^{2} \cdot (y^{5})^{2} = 4 \cdot y^{10} \] So, the simplified form is \( 4y^{10} \). Keep in mind that whenever you're raising a product to a power, you can distribute that exponent across the entire product!
