Express in exponent form.

a)$\frac{64}{125} $

b)$\quad \frac{-8}{342}$c)$625$

d) $\frac{16}{81}$

Solution:

a) $\frac{64}{125} $ 

$64  =  4 \times 4 \times 4  = 4^3$

$125  =  5 \times 5 \times 5 = 5^3$

$\frac{64}{125} $   =  $\left(\frac{4^{3}}{5^{3}}\right)$   

The powers are same, so

$\frac{64}{125} $    =  $ \left(\frac{4}{5}\right)^{3} $

b) $\quad \frac{-8}{342}$

$-8   =  -2  \times  -2  \times  -2  =  (-2)^3$    

$343  =  7 \times 7 \times 7  =  7^3$ 

$\quad \frac{-8}{342}$  =     $\left(\frac{-2^{3}}{7^{3}}\right)$   

$\quad \frac{-8}{342}$   =  $ \left(\frac{-2}{7}\right)^{3} $    

c)$625$

=  $5 \times 5 \times 5 \times 5$ 

= $5^4$   

$625 =  5^4$

d)$\frac{16}{81}$   

$16  =  2 \times 2 \times 2 \times 2  = 2^4$ 

$81  =  3 \times 3 \times 3 \times 3   =  3^4$ 

$\frac{16}{81}$    =  $\left(\frac{2^{4}}{3^{4}}\right)$     

$\frac{16}{81}$  = $ \left(\frac{2}{3}\right)^{4} $  

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Updated on: 10-Oct-2022

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