Algebra Examples

3^{6 - 3 x} = \frac{1}{27}

$3^{6 - 3 x} = \frac{1}{27}$

Step 1

Raise

27

$27$ to the power of

1

$1$ .

3^{6 - 3 x} = \frac{1}{27^{1}}

$3^{6 - 3 x} = \frac{1}{27^{1}}$

Step 2

Move

27^{1}

$27^{1}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

3^{6 - 3 x} = 27^{- 1}

$3^{6 - 3 x} = 27^{- 1}$

Step 3

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

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

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

Step 4

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

6 - 3 x = - 3

$6 - 3 x = - 3$

Step 5

Solve for

x

$x$ .

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Step 5.1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 5.1.1

Subtract

6

$6$ from both sides of the equation.

- 3 x = - 3 - 6

$- 3 x = - 3 - 6$

Step 5.1.2

Subtract

6

$6$ from

- 3

$- 3$ .

- 3 x = - 9

$- 3 x = - 9$

- 3 x = - 9

$- 3 x = - 9$

Step 5.2

Divide each term in

- 3 x = - 9

$- 3 x = - 9$ by

- 3

$- 3$ and simplify.

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Step 5.2.1

Divide each term in

- 3 x = - 9

$- 3 x = - 9$ by

- 3

$- 3$ .

\frac{- 3 x}{- 3} = \frac{- 9}{- 3}

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 5.2.2.1.1

Cancel the common factor.

\frac{- 3 x}{- 3} = \frac{- 9}{- 3}

$\frac{- 3 x}{- 3} = \frac{- 9}{- 3}$

Step 5.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 9}{- 3}

$x = \frac{- 9}{- 3}$

x = \frac{- 9}{- 3}

$x = \frac{- 9}{- 3}$

x = \frac{- 9}{- 3}

$x = \frac{- 9}{- 3}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide

- 9

$- 9$ by

- 3

$- 3$ .

x = 3

$x = 3$

x = 3

$x = 3$

x = 3

$x = 3$

x = 3

$x = 3$

3^{6 - 3 x} = \frac{1}{27}

$3^{6 - 3 x} = \frac{1}{27}$

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