Algebra Examples

$6^{- 2 x} \cdot 6^{- x} = \frac{1}{216}$

Step 1

Raise $216$ to the power of $1$ .

$6^{- 2 x} \cdot 6^{- x} = \frac{1}{216^{1}}$

Step 2

Move $216^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$6^{- 2 x} \cdot 6^{- x} = 216^{- 1}$

Step 3

Multiply $6^{- 2 x}$ by $6^{- x}$ by adding the exponents.

Tap for more steps...

Step 3.1

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

$6^{- 2 x - x} = 216^{- 1}$

Step 3.2

Subtract $x$ from $- 2 x$ .

$6^{- 3 x} = 216^{- 1}$

Step 4

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

$6^{- 3 x} = 6^{- 3}$

Step 5

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

$- 3 x = - 3$

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Divide $- 3$ by $- 3$ .

$x = 1$