Fill in the boxes-323-52-3-5-6 -3-2

Given, (3^2)^3×(5^2)^ 3/5^ 6 =[3^□]^2Now, =(3^2)^3×5^2× 3/5^ 6= (3^2)^3×5^ 6×5^6= (3^2)^3×5^ 6+6= (3^2)^3×5^0= (3^2)^3× 1= (3^2)^3=(3^3)^2Hence , the required ...

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Standard IX

Mathematics

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Question

Fill in the boxes.
$\frac{{(3^{2})}^{3} \times {(5^{2})}^{- 3}}{5^{- 6}} = {[3^{□}]}^{2}$

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Solution

Given, $\frac{{(3^{2})}^{3} \times {(5^{2})}^{- 3}}{5^{- 6}} = {[3^{□}]}^{2}$
Now,
$= \frac{{(3^{2})}^{3} \times 5^{2 \times - 3}}{5^{- 6}}$
$= {(3^{2})}^{3} \times 5^{- 6} \times 5^{6}$
$= {(3^{2})}^{3} \times 5^{- 6 + 6}$
$= {(3^{2})}^{3} \times 5^{0}$
$= {(3^{2})}^{3} \times 1$
$= {(3^{2})}^{3}$
$= {(3^{3})}^{2}$
Hence , the required value is $3$ .

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Fill in the boxes.323×52-35-6=3□2

Given, 323×52-35-6=3□2Now, =323×52×-35-6=323×5-6×56=323×5-6+6=323×50=323×1=323=332Hence , the required value is 3 .

Fill in the boxes.
$\frac{{(3^{2})}^{3} \times {(5^{2})}^{- 3}}{5^{- 6}} = {[3^{□}]}^{2}$