MCQ
If $abc = 0$, then find the value of $\Big\{(\text{x}^{\text{a}})^{\text{b}}\Big\}^{\text{c}}$
- ✓$1$
- B$a$
- C$b$
- D$c$
✓
Answer
Correct option: A.
$1$
Since,
$\Big\{(\text{x}^{\text{a}})^{\text{b}}\Big\}^{\text{c}}$
$=(\text{x}^{\text{a}})^{\text{bc}}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\text{x}^{\text{abc}}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\text{x}^{0}$ $[\text{As, abc}=0]$
$=1$ $[\text{As, }\text{x}^{0}=1]$
Hence, the correct alternative is option $(a)$.
$\Big\{(\text{x}^{\text{a}})^{\text{b}}\Big\}^{\text{c}}$
$=(\text{x}^{\text{a}})^{\text{bc}}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\text{x}^{\text{abc}}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\text{x}^{0}$ $[\text{As, abc}=0]$
$=1$ $[\text{As, }\text{x}^{0}=1]$
Hence, the correct alternative is option $(a)$.
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