Pre-Algebra Examples

$27^{x} = \frac{1}{81}$

Step 1

Raise $81$ to the power of $1$ .

$27^{x} = \frac{1}{81^{1}}$

Step 2

Move $81^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$27^{x} = 81^{- 1}$

Step 3

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

$3^{3 x} = 3^{- 4}$

Step 4

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

$3 x = - 4$

Step 5

Divide each term in $3 x = - 4$ by $3$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

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