Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
A expressão √[9](512³) simplifica a 8.
Solution
Para resolver a expressão √[9](512³), podemos proceder da seguinte forma:
1. Escreva a raiz como uma potência:
√[9](512³) = 512^(3/9) = 512^(1/3).
2. Note que 512 é igual a 8³, pois 8³ = 512. Assim, podemos substituir:
512^(1/3) = (8³)^(1/3) = 8^(3×(1/3)) = 8¹ = 8.
Portanto, o resultado da expressão é 8.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
Did you know that 512 can be expressed as a power of 2? That's right! \( 512 = 2^9 \). So when you take \( 512^3 \), it becomes \( (2^9)^3 = 2^{27} \). Now, calculating the ninth root of \( 2^{27} \) is a breeze, as it simplifies to \( 2^{27/9} = 2^3 = 8 \). If you're ever stuck in simplifying roots and exponents, remember the power laws! Always check if the base can be rewritten as a power of another number, and then apply your rules such as \( (a^m)^n = a^{mn} \) and \( \sqrt[n]{a^m} = a^{m/n} \). It's all about breaking it down into manageable parts, which can save you from common confusion with complex numbers!
