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Exponents — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsExponents1 Mark
MCQ
$\text{If abc} = 0,$ $\text{then}\frac{\Big\{(\text{x}^{\text{a}})^{\text{b}}\Big\}^{\text{c}}}{\Big\{(\text{x}^{\text{b}})^{\text{c}}\Big\}}=$
  • A
    $3$
  • B
    $0$
  • C
    $-1$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
$\frac{\Big\{(\text{x}^{\text{a}})^{\text{b}}\Big\}^{\text{c}}}{\Big\{(\text{x}^{\text{b}})^{\text{c}}\Big\}}$
$=\frac{(\text{x}^{\text{a}})^{\text{bc}}}{(\text{x}^{\text{b}})^{\text{ac}}}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\frac{\text{x}^{\text{abc}}}{\text{x}^{\text{abc}}}$ $[\text{As,}(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\frac{\text{x}^{0}}{\text{x}^{0}}$ $[\text{As, abc}=0]$
$=\frac{1}{1}$ $[\text{As, }\text{x}^{0}=1]$
$=1$
Hence, the correct alternative is option $(d).$

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