Question

Plz help me to solve it​

Answer 1

Answer:

it is your answer write it

Answer 2

Question:

If 9^x × 3^2 × (3^(-x/2))^-2 = 1/27, find x.

Answer:

-5/3

Step-by-step explanation:

Given 9^x × 3^2 × (3^(-x/2))^-2 = 1/27. We need to find out the value of x.

$\implies \sf{9}^{x} \times {3}^{2} \times ( {3}^{ \frac{ - x}{2} } )^{ - 2} = \dfrac{1}{27}$

Now, write all the numbers in the form of 3. Like: 9^x can be written as 3^2x and 27 as 3^3.

$\implies \sf{3}^{2x} \times {3}^{2} \times ( {3}^{ \frac{ - x}{2} } )^{ - 2} = \dfrac{1}{ {3}^{3}}$

Reciprocal of any number is written as 1^(-1). Therefore, 1/3^3 can be written as 3^(-3). So,

$\implies \sf{3}^{2x} \times {3}^{2} \times ( {3}^{ \frac{ - x}{2} } )^{ - 2} = {3}^{-3}$

(3^(-x/2))^-2 can be written as 3^(-2x/-2) or 3^x.

$\implies \sf{3}^{2x} \times {3}^{2} \times {3}^{x} = {3}^{-3}$

Law of exponents:

1. a^m × a^n = a^(m + n)
2. a^m/a^n = a^(m - n)
3. a^0 = 1
4. a^-1 = 1/a
5. (a^m)^n = a^(m × n)

Using above exponents rule, we can write 3^2x × 3^2 × 3^x as 3^(2x + 2 + x).

$\implies \sf{3}^{(2x + 2 + x)} = {3}^{(- 3)}$

$\implies \sf{3}^{(3x + 2)} = {3}^{( - 3)}$

On comparing we get,

$\implies\sf{3x+2=-3}$

$\implies\sf{3x=-3-2}$

$\implies\sf{3x=-5}$

$\implies\sf\boxed{x=\dfrac{-5}{3}}$

Therefore, the value of x is -5/3.