Question

find the value of x if (4/9)^4 * (4/9)^-7 = (16/36)^2x-1​

Answer 1

Answer:

x = -1

Step-by-step explanation:

We must know that,

(a/b)^m × (a/b)^n = (a/b)^(m+n)

Now,

(4/9)^4 × (4/9)^-7 = (16/36)^2x-1

(4/9)^(4 + -7) = (16/36)^2x-1

also,

16/36 = 4/9

so, (4/9)^-3 = (4/9)^2x-1

Now, bases are equal, so we can now equate the powers

-3 = 2x - 1

-3 + 1 = 2x

-2 = 2x

x = -2/2

x = -1

we can also check this

(4/9)^4 × (4/9)^-7 = (16/36)^2(-1) - 1

(4/9)^-3 = (4/9)^-2 - 1

(4/9)^-3 = (4/9)^-3

Thus,

LHS = RHS

Hope it helped and you understood it........All the best