Question

Find 'm' so that : (2/9)^-3 ×(2/9)^6 =(2/9)^2m-1 ........ please answer me

Answer 1

Answer:

n = 2

Step-by-step explanation:

Given: (2/9)⁻³ * (2/9)⁻⁶ = (2/9)²ⁿ⁻¹

⇒ (2/9)⁻³ ⁺ ⁶ = (2/9) ²ⁿ⁻¹

⇒ (2/9)³ = (2/9)²ⁿ⁻¹

⇒ 3 = 2n - 1

⇒ 3 + 1 = 2n

⇒ 4 = 2n

⇒ n = 2

Hope it helps!

Answer 2

Question:

Find 'm' so that,

$\displaystyle \left(\frac{2}{9}\right)^{-3} \times \left(\frac{2}{9}\right)^6=\left(\frac{2}{9}\right)^{2m-1}$

Answer:

We have to use the identity given below:

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

for any number a, m and n.

Now,

$\displaystyle \left(\frac{2}{9}\right)^{-3} \times \left(\frac{2}{9}\right)^6=\left(\frac{2}{9}\right)^{2m-1} \\ \\ \\ \left(\frac{2}{9}\right)^{-3+6}=\left(\frac{2}{9}\right)^{2m-1} \\ \\ \\ \left(\frac{2}{9}\right)^{3}=\left(\frac{2}{9}\right)^{2m-1} \\ \\ \\ \\ 3=2m-1 \\ \\ \\ 2m=3+1 \\ \\ \\ 2m=4 \\ \\ \\ m=\frac{4}{2} \\ \\ \\ m=\Large \textbf{2}$

Thus the value of m is 2.