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12 Mar 2025, 03:44
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
94% (00:27) correct
6%
(00:36)
wrong
based on 136
sessions
History
Date
Time
Result
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\(\sqrt [4] { (b^3)^8}=?\)
(A) \(b^2\)
(B) \(b^4\)
(C) \(b^6\)
(D) \(b^8\)
(E) \(b^{12}\)
(A) \(b^2\)
(B) \(b^4\)
(C) \(b^6\)
(D) \(b^8\)
(E) \(b^{12}\)
12 Mar 2025, 05:02
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Step 1: Simplify the Power Inside the Parentheses
Using the rule \(\left( a^m \right)^n = a^{m \cdot n}\):
\(\left( b^3 \right)^8 = b^{3 \cdot 8} = b^{24}\)
Now the expression becomes:
\(\text{Fourth root of } b^{24}\)
Step 2: Apply the Fourth Root
The fourth root of \(b^{24}\) can be written as:
\(\left( b^{24} \right)^{1/4} = b^{24 \cdot (1/4)} = b^{24/4} = b^6\)
Final Answer:
(C) \(b^6\)
Using the rule \(\left( a^m \right)^n = a^{m \cdot n}\):
\(\left( b^3 \right)^8 = b^{3 \cdot 8} = b^{24}\)
Now the expression becomes:
\(\text{Fourth root of } b^{24}\)
Step 2: Apply the Fourth Root
The fourth root of \(b^{24}\) can be written as:
\(\left( b^{24} \right)^{1/4} = b^{24 \cdot (1/4)} = b^{24/4} = b^6\)
Final Answer:
(C) \(b^6\)
