Question
Use the properties of exponents to simplify the expression: \( \left(a^{4}\right)^{3} a^{2} \) a.) \( a^{24} \) b.) \( a^{20} \) c.) \( a^{14} \) d.) \( a^{9} \)
Ask by Graham Rowe. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( a^{14} \), which is option c.)
Solution
To simplify the expression (a⁴)³ · a², follow these steps:
1. Apply the power of a power property: (a⁴)³ = a^(4×3) = a¹².
2. Now, multiply a¹² by a² using the product of powers property: a¹² · a² = a^(12+2) = a¹⁴.
Thus, the simplified expression is a¹⁴, which corresponds to option c.) a¹⁴.
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Simplify this solution Beyond the Answer
To simplify the expression \( \left(a^{4}\right)^{3} a^{2} \), we start by applying the power of a power property of exponents. This property states that \( (a^m)^n = a^{m \cdot n} \). So, \( \left(a^{4}\right)^{3} \) becomes \( a^{4 \cdot 3} = a^{12} \). Now, we can combine this with \( a^{2} \). According to the product of powers property, where \( a^m \cdot a^n = a^{m+n} \), we add the exponents: \( a^{12} a^{2} = a^{12 + 2} = a^{14} \). So the simplified expression is \( a^{14} \), which corresponds to option c.) \( a^{14} \).
