Solve for x (1/3)^x=27

${(\frac{1}{3})}^{x} = 27$

Step 1

Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{x}}{3^{x}} = 27$

Step 2

One to any power is one.

$\frac{1}{3^{x}} = 27$

Step 3

Move $3^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{- x} = 27$

Step 4

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

$3^{- x} = 3^{3}$

Step 5

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

$- x = 3$

Step 6

Divide each term in $- x = 3$ by $- 1$ and simplify.

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$x = - 3$