Solve for x (1/3)^2*(1/3)^x=1/729

${(\frac{1}{3})}^{2} \cdot {(\frac{1}{3})}^{x} = \frac{1}{729}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{1}{3})}^{2 + x} = \frac{1}{729}$

Create equivalent expressions in the equation that all have equal bases.

${(\frac{1}{3})}^{2 + x} = {(\frac{1}{3})}^{6}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 + x = 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$x = 6 - 2$

Subtract $2$ from $6$ .

$x = 4$