Math, asked by Jananii717, 10 months ago

express the following as powers of rational numbers of the following:- - 343/512, 32/243,-1/216, 729/1000

Answers

Answered by vedanshdarshan098
14

Here is your solution......

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Answered by sushiladevi4418
13

Answer:

\frac{-343}{512} = \frac{(-1)(7^{3}) }{2^{9} } 

\frac{32}{243}   = \frac{(2^{5}) }{3^{5} }

\frac{-1}{216}   = \frac{(-1)}{2^{3} \times 3^{3} }

\frac{729}{1000}   = \frac{3^{6} }{2^{3} \times 5^{3} }

Step-by-step explanation:

\frac{-343}{512} = \frac{(-1)(343)}{512}

On prime factorization,we get

343 = 7 x 7 x 7 ,  and 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

So, \frac{(-1)(343)}{512}  =  \frac{(-1)(7^{3}) }{2^{9} }  

Similarly,

\frac{32}{243}

On prime factorization,we get

32 = 2 x 2 x 2  x 2 x 2,  and 243 = 3 x 3 x 3 x 3 x 3

So, \frac{(32)}{243}  = \frac{(2^{5}) }{3^{5} }  

Now, \frac{-1}{216}

On prime factorization,we get

-1 = -1,  and 216 = 2 x 2 x 2 x 3 x 3 x 3

So, \frac{(-1)}{216}  = \frac{(-1)}{2^{3} \times 3^{3} }

Lastly, \frac{729}{1000}

On prime factorization,we get

729 = 3 x 3 x 3 x 3 x 3 x 3  ,  and 1000 = 2 x 2 x 2 x 5 x 5 x 5

So, \frac{(729)}{1000}  = \frac{3^{6} }{2^{3} \times 5^{3} }

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