If $$\frac{9^\text{m}×3^5×27^3}{3×81^4}=3^9$$​, then the value of m is:

Correct option is C

Given:

$$\frac{9^\text{m}×3^5×27^3}{3×81^4}=3^9$$

Concept Used:

a^m $$\times$$ aⁿ = a^{m + n}​

(a^m)ⁿ = a$$^{m\times n}$$​​

$$\frac{a^m}{a^n} =a^{m-n}$$​​

Solution:

$$\frac{9^\text{m}×3^5×27^3}{3×81^4}=3^9$$​​

​$$\frac{3^{2m} \times 3^5 \times 3^9}{3^1 \times 3^{16}} = 3^9$$​​

​$$\frac{3^{2m + 14}}{3^{17}} = 3^9$$​

​$$3^{2m + 14 - 17} = 3^9$$​

​$$3^{2m - 3} = 3^9$$​

2m - 3 = 9

2m = 12

m = 6