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Exponents and Powers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSExponents and Powers1 Mark
MCQ
If x be any integer different from zero and m, n be any integers, then $(x^m)^n$ is equal to:
  • A
    $\text{x}^{\text{m}+\text{n}}$
  • ✓
    $\text{x}^{\text{mn}}$
  • C
    $\text{x}^{\frac{\text{m}}{\text{n}}}$
  • D
    $\text{x}^{\text{m}-\text{n}}$
✓

Answer

Correct option: B.
$\text{x}^{\text{mn}}$
B.  $\text{x}^{\text{mn}}$
Solution:
Using law of exponents, $(\text{a}^{\text{m}})^{\text{n}}=(\text{a})^{\text{m}\times\text{n}}$ [$\because$ a is non-zero integer]
Similaly,
$(\text{x}^{\text{m}})^{\text{n}}=(\text{x})^{\text{m}\times\text{n}}$
$=(\text{x})^\text{mn}$

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