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

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

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

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

One to any power is one.

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

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

$3^{- x} = 27$

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

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

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

$- x = 3$

Multiply each term in $- x = 3$ by $- 1$

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

$(- x) \cdot - 1 = 3 \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = 3 \cdot - 1$

Multiply $x$ by $1$ .

$x = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$x = - 3$

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

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