Question
Simplify. How to... \[ \begin{array}{l}\text { Spotify - We... Apple idp.bowiestat... } \\ \text { Power rules with positive exponents: Multivariate products } \\ \text { Write your answer without parentheses. } \\ \left.\text { Si } 3 a^{4} b^{3}\right)^{4}\end{array} \]
Ask by Harmon King. in the United States
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
81a¹⁶b¹²
Solution
To simplify (3a⁴b³)⁴, raise each factor inside the parentheses to the fourth power:
1. 3⁴ = 81
2. a⁴ raised to the fourth power gives a^(4×4) = a¹⁶
3. b³ raised to the fourth power gives b^(3×4) = b¹²
So, the simplified expression is:
81a¹⁶b¹²
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To simplify the expression \((3a^{4}b^{3})^{4}\), you apply the power of a product rule, which states that \((xy)^n = x^n y^n\). That means you can raise each part inside the parentheses to the fourth power. Therefore, we have: 1. Raise the coefficient \(3\) to the power of \(4\): \(3^{4} = 81\). 2. Raise \(a^{4}\) to the power of \(4\): \((a^{4})^{4} = a^{16}\). 3. Raise \(b^{3}\) to the power of \(4\): \((b^{3})^{4} = b^{12}\). Putting it all together, the simplified expression is: \[ 81a^{16}b^{12} \] No parentheses are needed, so the final answer is: \[ 81a^{16}b^{12} \]
