Algebra Examples

$(3 \frac{x}{2}) (3 \frac{x}{4}) = 3^{6}$

Step 1

Simplify $3 (\frac{x}{2}) \cdot (3 (\frac{x}{4}))$ .

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Step 1.1

Combine $3$ and $\frac{x}{2}$ .

$\frac{3 x}{2} \cdot (3 (\frac{x}{4})) = 3^{6}$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \frac{3 x}{2} \frac{x}{4} = 3^{6}$

Step 1.3

Multiply $3 \frac{3 x}{2}$ .

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Step 1.3.1

Combine $3$ and $\frac{3 x}{2}$ .

$\frac{3 (3 x)}{2} \cdot \frac{x}{4} = 3^{6}$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{9 x}{2} \cdot \frac{x}{4} = 3^{6}$

Step 1.4

Multiply $\frac{9 x}{2} \cdot \frac{x}{4}$ .

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Step 1.4.1

Multiply $\frac{9 x}{2}$ by $\frac{x}{4}$ .

$\frac{9 x \cdot x}{2 \cdot 4} = 3^{6}$

Step 1.4.2

Raise $x$ to the power of $1$ .

$\frac{9 (x^{1} x)}{2 \cdot 4} = 3^{6}$

Step 1.4.3

Raise $x$ to the power of $1$ .

$\frac{9 (x^{1} x^{1})}{2 \cdot 4} = 3^{6}$

Step 1.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 x^{1 + 1}}{2 \cdot 4} = 3^{6}$

Step 1.4.5

Add $1$ and $1$ .

$\frac{9 x^{2}}{2 \cdot 4} = 3^{6}$

Step 1.4.6

Multiply $2$ by $4$ .

$\frac{9 x^{2}}{8} = 3^{6}$

Step 2

Raise $3$ to the power of $6$ .

$\frac{9 x^{2}}{8} = 729$

Step 3

Multiply both sides of the equation by $\frac{8}{9}$ .

$\frac{8}{9} \cdot \frac{9 x^{2}}{8} = \frac{8}{9} \cdot 729$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{8}{9} \cdot \frac{9 x^{2}}{8}$ .

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Step 4.1.1.1

Combine.

$\frac{8 (9 x^{2})}{9 \cdot 8} = \frac{8}{9} \cdot 729$

Step 4.1.1.2

Cancel the common factor of $8$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{8 (9 x^{2})}{9 \cdot 8} = \frac{8}{9} \cdot 729$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{9 x^{2}}{9} = \frac{8}{9} \cdot 729$

Step 4.1.1.3

Cancel the common factor of $9$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{8}{9} \cdot 729$

Step 4.1.1.3.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{8}{9} \cdot 729$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{8}{9} \cdot 729$ .

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Step 4.2.1.1

Cancel the common factor of $9$ .

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Step 4.2.1.1.1

Factor $9$ out of $729$ .

$x^{2} = \frac{8}{9} \cdot (9 (81))$

Step 4.2.1.1.2

Cancel the common factor.

$x^{2} = \frac{8}{9} \cdot (9 \cdot 81)$

Step 4.2.1.1.3

Rewrite the expression.

$x^{2} = 8 \cdot 81$

Step 4.2.1.2

Multiply $8$ by $81$ .

$x^{2} = 648$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{648}$

Step 6

Simplify $\pm \sqrt{648}$ .

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Step 6.1

Rewrite $648$ as $18^{2} \cdot 2$ .

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Step 6.1.1

Factor $324$ out of $648$ .

$x = \pm \sqrt{324 (2)}$

Step 6.1.2

Rewrite $324$ as $18^{2}$ .

$x = \pm \sqrt{18^{2} \cdot 2}$

Step 6.2

Pull terms out from under the radical.

$x = \pm 18 \sqrt{2}$

Step 7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 7.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 18 \sqrt{2}$

Step 7.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 18 \sqrt{2}$

Step 7.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 18 \sqrt{2}, - 18 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 18 \sqrt{2}, - 18 \sqrt{2}$

Decimal Form:

$x = 25.45584412 \dots, - 25.45584412 \dots$