ABC26GN1901 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2010 · Marks: · Difficulty:
$(6)^{4} \div(36)^{3} \times 216=6^{(?-5)}$
(a)1
(b)4
(c)6
(d)7
(e)None of these
Answer
Explanation
Let $6^{4} \div(36)^{3} \times 216=6^{(x-5)}$. Then, $6^{(x-5)}=6^{4} \div\left(6^{2}\right)^{3} \times 6^{3}$ $$\begin{aligned} & =6^{4} \div 6^{(2 \times 3)} \times 6^{3}=6^{4} \div 6^{6} \times 6^{3}=6^{(4-6+3)}=6 \\ & \Rightarrow \quad x-5=1 \Rightarrow x=6 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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