Algebra Examples

$\frac{6^{\frac{1}{4}}}{36^{- \frac{x}{2}}} = 1$

Step 1

Multiply both sides by $36^{- \frac{x}{2}}$ .

$\frac{6^{\frac{1}{4}}}{36^{- \frac{x}{2}}} \cdot 36^{- \frac{x}{2}} = 1 \cdot 36^{- \frac{x}{2}}$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $36^{- \frac{x}{2}}$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{6^{\frac{1}{4}}}{36^{- \frac{x}{2}}} \cdot 36^{- \frac{x}{2}} = 1 \cdot 36^{- \frac{x}{2}}$

Step 2.1.1.2

Rewrite the expression.

$6^{\frac{1}{4}} = 1 \cdot 36^{- \frac{x}{2}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $36^{- \frac{x}{2}}$ by $1$ .

$6^{\frac{1}{4}} = 36^{- \frac{x}{2}}$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $36^{- \frac{x}{2}} = 6^{\frac{1}{4}}$ .

$36^{- \frac{x}{2}} = 6^{\frac{1}{4}}$

Step 3.2

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

$6^{2 (- \frac{x}{2})} = 6^{\frac{1}{4}}$

Step 3.3

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

$2 (- \frac{x}{2}) = \frac{1}{4}$

Step 3.4

Solve for $x$ .

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Step 3.4.1

Cancel the common factor of $2$ .

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Step 3.4.1.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$2 \frac{- x}{2} = \frac{1}{4}$

Step 3.4.1.2

Cancel the common factor.

$2 \frac{- x}{2} = \frac{1}{4}$

Step 3.4.1.3

Rewrite the expression.

$- x = \frac{1}{4}$

Step 3.4.2

Divide each term in $- x = \frac{1}{4}$ by $- 1$ and simplify.

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Step 3.4.2.1

Divide each term in $- x = \frac{1}{4}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{1}{4}}{- 1}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{1}{4}}{- 1}$

Step 3.4.2.2.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{4}}{- 1}$

Step 3.4.2.3

Simplify the right side.

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Step 3.4.2.3.1

Move the negative one from the denominator of $\frac{\frac{1}{4}}{- 1}$ .

$x = - 1 \cdot \frac{1}{4}$

Step 3.4.2.3.2

Rewrite $- 1 \cdot \frac{1}{4}$ as $- \frac{1}{4}$ .

$x = - \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{4}$

Decimal Form:

$x = - 0.25$