Question

the one who will solve it perfectly will get 78 coins and I will mark it as BRAINLIEST !!!! समझ में आया क्या ​

Answer 1

Answer:

let p be the number in empty block.

(3/2)^8 x (9/4)^p =(3/2)^28

=>(3/2)^8 x (3^2/2^2)^p =(3/2)^28

=>(3/2)^8 x (3/2)^2p =(3/2)^28.

=>(3/2)^(8+2p) =(3/2)^28. (formula a^m x a^n = a^(m+n)

compare both sides

8+2p=28

2p=28-8

2p=20

p=10

the number in empty box is 10.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the formula of indices that :

1.

${a}^{m} \times {a}^{n} = {a}^{m + n}$

2.

${ \: ({a}^{m} )}^{n} = {a}^{mn}$

3.

${a}^{m} = {a}^{n} \: \: implies \: \: m = n$

GIVEN

$\sf{ \:Taking \: x \: as \: missing \: term \: }$

$\displaystyle \: { \bigg( \: \frac{3}{2} \bigg)}^{8} \times { \bigg( \: \frac{9}{4} \bigg)}^{x} = { \bigg( \: \frac{3}{2} \bigg)}^{28}$

TO DETERMINE

The value of x

EVALUATION

$\displaystyle \: { \bigg( \: \frac{3}{2} \bigg)}^{8} \times { \bigg( \: \frac{9}{4} \bigg)}^{x} = { \bigg( \: \frac{3}{2} \bigg)}^{28}$

$\implies \: \displaystyle \: { \bigg( \: \frac{3}{2} \bigg)}^{8} \times { \bigg[ \: { \bigg( \: \frac{3}{2} \bigg) }^{2} \bigg] }^{x} = { \bigg( \: \frac{3}{2} \bigg)}^{28}$

$\implies \: \displaystyle \: { \bigg( \: \frac{3}{2} \bigg)}^{8} \times { \bigg( \: \frac{3}{2} \bigg)}^{2x} = { \bigg( \: \frac{3}{2} \bigg)}^{28}$

$\implies \: \displaystyle \: { \bigg( \: \frac{3}{2} \bigg)}^{8 + 2x} = { \bigg( \: \frac{3}{2} \bigg)}^{28}$

$\implies \: 8 + 2x = 28$

$\implies \: 2x = 20$

$\implies \: x = 10$

RESULT

$\sf{ \boxed{ \: The \: missing \: term \: is \: 10 \: }}$