MCQ
$\Big\{(33)^2-(31)^2\Big\}^{\frac{5}{7}}$
- A$64$
- B$16$
- ✓$32$
- D$4$
✓
Answer
Correct option: C.
$32$
Since,
$\Big\{(33)^2-(31)^2\Big\}^{\frac{5}{7}}$
$=\{1089-961\}^{\frac{5}{7}}$
$=\{128\}^{\frac{5}{7}}$
$=\{2^7\}^{\frac{5}{7}}$
$=2^{7\times\frac{5}{7}}$$[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=2^5$
$=32$
Hence, the correct alternative is option $(c).$
$\Big\{(33)^2-(31)^2\Big\}^{\frac{5}{7}}$
$=\{1089-961\}^{\frac{5}{7}}$
$=\{128\}^{\frac{5}{7}}$
$=\{2^7\}^{\frac{5}{7}}$
$=2^{7\times\frac{5}{7}}$$[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=2^5$
$=32$
Hence, the correct alternative is option $(c).$
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