Question
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Answer
\( \left(x^{3}\right)^{2} = x^{6} \)
Solution
b) \( \left(x^{3}\right)^{2} = x^{6} \)
**Explicación:**
Cuando elevamos una potencia a otra potencia, multiplicamos los exponentes. En este caso:
\[
\left(x^{3}\right)^{2} = x^{3 \times 2} = x^{6}
\]
Por lo tanto, \( \left(x^{3}\right)^{2} \) simplificado es \( x^{6} \).
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Simplify this solution Beyond the Answer
To evaluate \( \left(x^{3}\right)^{2} \), you can apply the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\). So, in this case, you multiply the exponents: \(3 \cdot 2 = 6\). Therefore, \( \left(x^{3}\right)^{2} = x^{6} \). Now, if you're looking for a practical way to remember exponent rules: picture a party – every time someone brings a plus one (an exponent), the number of guests (or total exponents) multiplies! Just as a single guest turns into a pair, your \(x^3\) becomes \(x^6\) after bringing a plus one in the exponent game!
