Question

plz answer the ques guys ​

Answer 1

Given :

• $\sf\:x ~= ~\left(\frac{3}{4}\right)^{3}~\left(\frac{4}{3}\right)^{5}$

• $\sf\:y~=~(2^{-2}+3^{-2}+4^{-1})$

To find :

• Value of x + y
• Value of x/y

Solution :

Simplifying the given value of x,

$\sf\to\:x ~= ~\left(\frac{3}{4}\right)^{3}~\left(\frac{4}{3}\right)^{5}$

$\sf\to\:x ~= ~\frac{\left(3\right)^{3}}{\left(4\right)^{3}}~\frac{\left(4\right)^{5}}{\left(3\right)^{5}}$

$\sf\to\:x ~= ~\left(\frac{27}{64}\right)~\left(\frac{1024}{243}\right)$

$\sf\to\:x ~= \frac{27648}{15552}$

Now again simplifying the value of y,

$\sf\:y~=~(2^{-2}+3^{-2}+4^{-1})$

$\sf\to\:y~=~(\cancel{4}+9-\cancel{4})$

$\sf\to\:y~=~9$

Now calculating the value of :

(i) $\tt\:x+y$

$\tt\twoheadrightarrow\:\frac{27648}{15552}+9$

$\tt\twoheadrightarrow\:\frac{27648+139968}{15552}$

$\tt\twoheadrightarrow\:\frac{167616}{15552}$

$\bf\twoheadrightarrow\:10.7$

(ii) $\tt\:\frac{x}{y}$

$\tt\twoheadrightarrow\:\frac{\frac{27648}{15552}}{9}$

$\tt\twoheadrightarrow\:\frac{27648}{15552} \times \frac{1}{9}$

$\tt\twoheadrightarrow\:\frac{27648}{139968}$

$\bf\twoheadrightarrow\:0.197$

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