Solve for x (1/3)^(-x)>27^(2x+1)

${(\frac{1}{3})}^{- x} > 27^{2 x + 1}$

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

$\frac{1^{- x}}{3^{- x}} > 27^{2 x + 1}$

One to any power is one.

$\frac{1}{3^{- x}} > 27^{2 x + 1}$

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

$3^{x} > 27^{2 x + 1}$

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

$3^{x} > 3^{3 (2 x + 1)}$

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

$x > 3 (2 x + 1)$

Solve for $x$ .

Simplify $3 (2 x + 1)$ .

Apply the distributive property.

$x > 3 (2 x) + 3 \cdot 1$

Multiply.

Multiply $2$ by $3$ .

$x > 6 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$x > 6 x + 3$

Move all terms containing $x$ to the left side of the inequality.

Subtract $6 x$ from both sides of the inequality.

$x - 6 x > 3$

Subtract $6 x$ from $x$ .

$- 5 x > 3$

Divide each term in $- 5 x > 3$ by $- 5$ and simplify.

Divide each term in $- 5 x > 3$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} < \frac{3}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} < \frac{3}{- 5}$

Divide $x$ by $1$ .

$x < \frac{3}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{3}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{3}{5}$

Interval Notation:

$(- \infty, - \frac{3}{5})$

Solve for x (1/3)^(-x)>27^(2x+1)

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