If _b a=p, _d c=2 p and _f e=3 p , then what is ( ace )^ (1)/(p) equal to?

Correct answer: A. b d^2 f^3 aligned _b a & =P a=b^ P _d c & =2 P c=d^ 2 P _f e & =3 P e=f^ 3 P (a c e)^ 1 P & =(b^ P d^ 2 P f^ 3 P )^ 1 P & =b d^2 f^3. aligned

NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Basics of Mathematics

NDA 2024 · Mathematics · Basics of Mathematics

If _b a=p, _d c=2 p and _f e=3 p , then what is ( ace )^ (1)/(p)...

\log _b a=p, \log _d c=2 p

and

\log _f e=3 p

, then what is

(\text{ ace })^{\frac{1}{p}}

equal to?

Options

A $b d^2 f^3$
B $b d f$
C $b^3 d^2 f$
D $b^2 d^2 f^2$

Correct answer

A. $b d^2 f^3$

Step-by-step solution

\begin{aligned} \because \quad \log _b a & =\mathrm{P} \Rightarrow a=b^{\mathrm{P}} \\ \log _d c & =2 \mathrm{P} \Rightarrow c=d^{2 \mathrm{P}} \\ \log _f e & =3 \mathrm{P} \Rightarrow e=f^{3 \mathrm{P}} \\ (a c e)^{\frac{1}{\mathrm{P}}} & =\left(b^{\mathrm{P}} d^{2 \mathrm{P}} f^{3 \mathrm{P}}\right)^{\frac{1}{\mathrm{P}}} \\ & =b d^2 f^3.\end{aligned}

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