Question

if m/n=(3/4)²×(3/4)-⁴ then find (m/n)-²​

Answer 1

Answer:

m/n= (3/4)^2 ×( 3/4)^-4

m/n =(3/4)^-2

(m/n)^-2= ((3/4)^-2)^-2 = (3/4)^4

=3^4/4^4

=81/256

Answer 2

Answer:

$\purple{\star} \: {\large{\underline{\boxed{\tt{\dfrac{81}{256}}}}}}$

Step-by-step explanation:

★ Value of $\large{\sf{\dfrac{m}{n} = \bigg(\dfrac{3}{4}\bigg)^{2} \times \bigg(\dfrac{3}{4}\bigg)^{ - 4}}}$

• When two same values with different exponents are Multiplied then the exponents are added together while the same value is written only one time.

$\large{\leadsto{\sf{\bigg(\dfrac{3}{4}\bigg)^{2 + ( - 4)}}}}$

$\large{\leadsto{\sf{\bigg(\dfrac{3}{4}\bigg)^{2 - 4}}}}$

$\large{\leadsto{\sf{\bigg(\dfrac{3}{4}\bigg)^{ - 2}}}}$

$\large{\leadsto{\sf{\bigg(\dfrac{4}{3}\bigg)^{2}}}}$

$\large{\leadsto{\sf{\bigg(\dfrac{4 \times 4}{3 \times 3}\bigg)}}}$

$\large{\leadsto{\sf{\dfrac{16}{9}}}}$

Now,

$\large{\sf{\bigg(\dfrac{m}{n}\bigg)^{ - 2}}}$

• Substituting the values,

$\large{\rightarrow{\sf{\bigg(\dfrac{16}{9}\bigg)^{ - 2}}}}$

$\large{\rightarrow{\sf{\bigg(\dfrac{9}{16}\bigg)^{2}}}}$

$\large{\rightarrow{\sf{\dfrac{9 \times 9}{16 \times 16}}}}$

$\large{\gray{\rightarrow{\sf{\dfrac{81}{256}}}}}$

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$\diamond \: {\large{\underline{\underline{\sf{Negative \: Exponent \: Rule:-}}}}}$

➛ To change a negative exponent to positive we need to flip the value into a reciprocal.