Algebra Examples

$6^{4 x + 7} \cdot \frac{1}{36} = 1$

Step 1

Combine $6^{4 x + 7}$ and $\frac{1}{36}$ .

$\frac{6^{4 x + 7}}{36} = 1$

Step 2

Multiply both sides by $36$ .

$\frac{6^{4 x + 7}}{36} \cdot 36 = 1 \cdot 36$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $36$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{6^{4 x + 7}}{36} \cdot 36 = 1 \cdot 36$

Step 3.1.1.2

Rewrite the expression.

$6^{4 x + 7} = 1 \cdot 36$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $36$ by $1$ .

$6^{4 x + 7} = 36$

Step 4

Solve for $x$ .

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Step 4.1

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

$6^{4 x + 7} = 6^{2}$

Step 4.2

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

$4 x + 7 = 2$

Step 4.3

Solve for $x$ .

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Step 4.3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.3.1.1

Subtract $7$ from both sides of the equation.

$4 x = 2 - 7$

Step 4.3.1.2

Subtract $7$ from $2$ .

$4 x = - 5$

Step 4.3.2

Divide each term in $4 x = - 5$ by $4$ and simplify.

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Step 4.3.2.1

Divide each term in $4 x = - 5$ by $4$ .

$\frac{4 x}{4} = \frac{- 5}{4}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

Cancel the common factor of $4$ .

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 5}{4}$

Step 4.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{4}$

Step 4.3.2.3

Simplify the right side.

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Step 4.3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{4}$

Decimal Form:

$x = - 1.25$

Mixed Number Form:

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