Question

Plz solve and send asap

Answer 1

Answer:

2. $\left(\dfrac{m}{n}\right)^{-1}$=0.0263671875

3. (a) x = 3

Given:

☞$\dfrac{m}{n}\:=\:\left(\dfrac{3}{4}\right)^{-5}\:\times\:\left(\dfrac{1}{3}\right)^{-2}$

☞$\left[\left(\dfrac{4}{5}\right)^3\right]^{-2}\:=\:\left(\dfrac{4}{5}\right)^{2x}$

To Calculate:

2. $\left(\dfrac{m}{n}\right)^{-1}$

3. (a) Find the value of x.

Explanation:

2)

$\dfrac{m}{n} = \left( \dfrac{3}{4} \right)^{ - 5} \times \left( \dfrac{1}{3} \right)^{ - 2}$

$\dfrac{m}{n} = \left(\dfrac{4}{3} \right) ^{5} \times {3}^{2}$

$\dfrac{m}{n} = \dfrac{4^{5} }{3^{5 - 2} }$

$\dfrac{m}{n} = \frac{ {4}^{5} }{ {3}^{3} }$

$\dfrac{m}{n} = \dfrac{1024}{27}$

To Calculate:

$\left(\dfrac{m}{n}\right)^{-1}$

$\left( \dfrac{m}{n} \right)^{ - 1} = \left(\dfrac{1024}{27}\right)^{ - 1} \: \: \: \: \: \: \: \\ \left( \frac{m}{n} \right)^{ - 1} = \left( \frac{27}{1024} \right) \: \: \: \: \: \: \: \: \: \: \: \\ \left( \frac{m}{n} \right)^{ - 1} = 0.0263671875$

3) (a)

$\left[\left( \dfrac{4}{5} \right)^{ - 3} \right] ^{2} = \left( \dfrac{4}{5}\right ) ^{2x} \\ \left[ \dfrac{4}{5} \right]^{ - 6} =\left ( \frac{4}{5} \right)^{2x} \: \: \: \: \: \: \: \: \: \:$

Comparing powers on both sides, we get:

2x = -6

x = -3

Therefore, the answer is:

☞$\left(\dfrac{m}{n}\right)^{-1}$=0.0263671875

☞x = -3