Question

If $a^{2m–2}\cdot b^{3n–3}\cdot c^{4p–4}=abc$, where a, b, c are natural numbers, then equals

• A. $\frac{2}{5}$
• B. $\frac{5}{2}$
• C. 1
• D. $\frac{49}{12}$

Answer 1

The correct option is A $\frac{2}{5}$

Given: $a^{2m–2}\cdot b^{3n–3}\cdot c^{4p–4}=abc$, where a, b, c ∈ ℕ.
$\Rightarrow 2m-2=1,3n-3=1,4p-4=1$
$\Rightarrow m=\frac{3}{2},n=\frac{4}{3},p=\frac{5}{4}$
$\Rightarrow mnp=\frac{3}{2}\times \frac{4}{3}\times \frac{5}{4}=\frac{5}{2}$
$\Rightarrow \frac{1}{mnp}=\frac{2}{5}$
Hence, the correct answer is option (a).