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Question
Math
Posted about 1 month ago

Select the equivalent expression.
(3366)3=?
\left(3^{3} \cdot 6^{6}\right)^{-3}=?


Choose 1 answer:
(A) 61839\frac{6^{18}}{3^{9}}
(B) 39618\frac{3^{9}}{6^{18}}
(c) 139618\frac{1}{3^{9} \cdot 6^{18}}
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Answer from Sia
Posted about 1 month ago
Solution by Steps
step 2
Apply the negative exponent rule: (3366)3=1(3366)3\left(3^{3} \cdot 6^{6}\right)^{-3} = \frac{1}{\left(3^{3} \cdot 6^{6}\right)^{3}}
step 3
Simplify the exponent: (3366)3=333663=39618\left(3^{3} \cdot 6^{6}\right)^{3} = 3^{3 \cdot 3} \cdot 6^{6 \cdot 3} = 3^{9} \cdot 6^{18}
step 4
Combine the results: 139618\frac{1}{3^{9} \cdot 6^{18}}
C
Key Concept
Negative Exponent Rule
Explanation
When an expression with a product is raised to a negative exponent, it is equivalent to the reciprocal of the expression raised to the positive exponent.

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