Algebra Examples

$\frac{27^{\frac{1}{4}}}{3^{\frac{x}{4}}} = 1$

Step 1

Multiply both sides by $3^{\frac{x}{4}}$ .

$\frac{27^{\frac{1}{4}}}{3^{\frac{x}{4}}} \cdot 3^{\frac{x}{4}} = 1 \cdot 3^{\frac{x}{4}}$

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 $3^{\frac{x}{4}}$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{27^{\frac{1}{4}}}{3^{\frac{x}{4}}} \cdot 3^{\frac{x}{4}} = 1 \cdot 3^{\frac{x}{4}}$

Step 2.1.1.2

Rewrite the expression.

$27^{\frac{1}{4}} = 1 \cdot 3^{\frac{x}{4}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3^{\frac{x}{4}}$ by $1$ .

$27^{\frac{1}{4}} = 3^{\frac{x}{4}}$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $3^{\frac{x}{4}} = 27^{\frac{1}{4}}$ .

$3^{\frac{x}{4}} = 27^{\frac{1}{4}}$

Step 3.2

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

$3^{\frac{x}{4}} = 3^{3 (\frac{1}{4})}$

Step 3.3

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

$\frac{x}{4} = 3 (\frac{1}{4})$

Step 3.4

Solve for $x$ .

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Step 3.4.1

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (3 (\frac{1}{4}))$

Step 3.4.2

Simplify both sides of the equation.

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Step 3.4.2.1

Simplify the left side.

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Step 3.4.2.1.1

Cancel the common factor of $4$ .

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Step 3.4.2.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (3 (\frac{1}{4}))$

Step 3.4.2.1.1.2

Rewrite the expression.

$x = 4 (3 (\frac{1}{4}))$

Step 3.4.2.2

Simplify the right side.

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Step 3.4.2.2.1

Simplify $4 (3 (\frac{1}{4}))$ .

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Step 3.4.2.2.1.1

Combine $3$ and $\frac{1}{4}$ .

$x = 4 (\frac{3}{4})$

Step 3.4.2.2.1.2

Cancel the common factor of $4$ .

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Step 3.4.2.2.1.2.1

Cancel the common factor.

$x = 4 (\frac{3}{4})$

Step 3.4.2.2.1.2.2

Rewrite the expression.

$x = 3$