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Q) Express cach of the following in exponuntial for
a) $\frac{729}{125}$
b)$\frac{1296}{2401}$
Solution:
a) $\frac{-729}{125}$
$-729 = -9 \times - 9 \times -9 = (-9)^3$
$125 = 5 \times 5 \times 5 = 5^3$
$\frac{-729}{125}$ = $\frac{-9^{3}}{5^{3}}$
= $\left(\frac{-9}{5}\right)^{3}$
b) $\frac{1296}{2401}$
$1296 = 6 \times 6 \times 6 \times 6 = 6^4 $
$2401 = 7 \times 7 \times 7 \times 7 = 7^4 $
$\frac{1296}{2401}$= $\frac{6^{4}}{7^{4}}$
= $\left(\frac{6}{7}\right)^{4}$
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