If a = 3^ -3 - 3^3 and b = 3^3 - 3^ -3 , then a b - b a =

MCQ

If $a = 3^{-3} - 3^3$ and $b = 3^3 - 3^{-3},$ then $\frac{\text{a}}{\text{b}}-\frac{\text{b}}{\text{a}}=$

✓
$0$
B
$1$
C
$-1$
D
$2$

✓

Answer

Correct option: A.

$0$

Since,
$\text{a}=3^{-3}-3^3$
$=\frac{1}{3^3}-3^3$ $\Big(\text{As},\text{x}^{-\text{m}}=\frac{1}{\text{x}^{\text{m}}}\Big)$
$=\frac{1}{27}-\frac{27}{1}$
$=\frac{1}{27}-\frac{27\times27}{1\times27}$
$=\frac{1}{27}-\frac{729}{27}$
$=\frac{1-729}{27}$
$=\frac{-728}{27}$
Also, $\text{b}=3^3-3^{-3}$
$=3^3-\frac{1}{3^3}$ $\Big(\text{As, }\text{x}^{-\text{m}}=\frac{1}{\text{x}^{\text{m}}}\Big)$
$=\frac{27}{1}-\frac{1}{27}$
$=\frac{27\times27}{1\times27}-\frac{1}{27}$
$=\frac{729}{27}-\frac{1}{27}$
$=\frac{729-1}{27}$
$=\frac{728}{27}$
Now,
$\frac{\text{a}}{\text{b}}-\frac{\text{b}}{\text{a}}$
$=\frac{\Big(\frac{-728}{27}\Big)}{\Big(\frac{728}{27}\Big)}-\frac{\Big(\frac{728}{27}\Big)}{\Big(\frac{-728}{27}\Big)}$
$=(-1)-(-1)$
$=-1+1$
$=0$
Hence, the correct alternative is option $(a)$.

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