Question

Without using a calculator, find the value of x such that 9(3^x)^3= square root(1/27^2)

So the answers show that 3^2(3^3x)= square root(1/3^3x)

Why is it 1/3^3x? Wasn't it 1/27^2? Please explain clearly to me, thks!

Answer 1

Your observation appears correct; the right side is 1/√(27^2)

(3^x)^3 = 3^(3*x) = 3^(3x)
9 = 3^2, so
9*3^(3x) = 3^2 * 3^(3x) = 3^(3x+2)

Now, on the right, for any value n,
√(n^2) = n, so we have

1/27 = 3^-2

So, we want x such that

3^(3x+2) = 3^-2
3x+2 = -2
3x = -4
x = -4/3