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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Updated on: 10-Oct-2022

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