MCQ
Simplify $\Big(\frac{7}{9}\Big)^{-9}\times\Big(\frac{9}{7}\Big)^{-7}$ and find the value.
- A$\frac{16}{25}$
- B$\frac{18}{14}$
- ✓$\frac{81}{49}$
- D$\frac{49}{81}$
✓
Answer
Correct option: C.
$\frac{81}{49}$
$\Big(\frac{7}{9}\Big)^{-9}\times\Big(\frac{9}{7}\Big)^{-7}=\frac{7^{-9}}{9^{-9}}\times\frac{9^{-7}}{7^{-7}}$
$=\frac{9^9}{7^9}\times\frac{7^7}{9^7}$
$=\frac{9^2}{7^2}$
$=\frac{81}{49}$
$=\frac{9^9}{7^9}\times\frac{7^7}{9^7}$
$=\frac{9^2}{7^2}$
$=\frac{81}{49}$
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