Algebra Examples

$8^{- \frac{x}{3}} = 4$

Step 1

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

$2^{3 (- \frac{x}{3})} = 2^{2}$

Step 2

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

$3 (- \frac{x}{3}) = 2$

Step 3

Solve for $x$ .

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$3 \frac{- x}{3} = 2$

Step 3.1.2

Cancel the common factor.

$3 \frac{- x}{3} = 2$

Step 3.1.3

Rewrite the expression.

$- x = 2$

Step 3.2

Divide each term in $- x = 2$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $2$ by $- 1$ .

$x = - 2$