Pre-Algebra Examples

$9 x^{22} = 8 x$

Step 1

Subtract $8 x$ from both sides of the equation.

$9 x^{22} - 8 x = 0$

Step 2

Factor $x$ out of $9 x^{22} - 8 x$ .

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Step 2.1

Factor $x$ out of $9 x^{22}$ .

$x (9 x^{21}) - 8 x = 0$

Step 2.2

Factor $x$ out of $- 8 x$ .

$x (9 x^{21}) + x \cdot - 8 = 0$

Step 2.3

Factor $x$ out of $x (9 x^{21}) + x \cdot - 8$ .

$x (9 x^{21} - 8) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$9 x^{21} - 8 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $9 x^{21} - 8$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $9 x^{21} - 8$ equal to $0$ .

$9 x^{21} - 8 = 0$

Step 5.2

Solve $9 x^{21} - 8 = 0$ for $x$ .

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Step 5.2.1

Add $8$ to both sides of the equation.

$9 x^{21} = 8$

Step 5.2.2

Divide each term in $9 x^{21} = 8$ by $9$ and simplify.

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Step 5.2.2.1

Divide each term in $9 x^{21} = 8$ by $9$ .

$\frac{9 x^{21}}{9} = \frac{8}{9}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $9$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{9 x^{21}}{9} = \frac{8}{9}$

Step 5.2.2.2.1.2

Divide $x^{21}$ by $1$ .

$x^{21} = \frac{8}{9}$

Step 5.2.3

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

$x = \sqrt[21]{\frac{8}{9}}$

Step 5.2.4

Simplify $\sqrt[21]{\frac{8}{9}}$ .

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Step 5.2.4.1

Rewrite $\sqrt[21]{\frac{8}{9}}$ as $\frac{\sqrt[21]{8}}{\sqrt[21]{9}}$ .

$x = \frac{\sqrt[21]{8}}{\sqrt[21]{9}}$

Step 5.2.4.2

Simplify the numerator.

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Step 5.2.4.2.1

Rewrite $8$ as $2^{3}$ .

$x = \frac{\sqrt[21]{2^{3}}}{\sqrt[21]{9}}$

Step 5.2.4.2.2

Rewrite $\sqrt[21]{2^{3}}$ as $\sqrt[7]{\sqrt[3]{2^{3}}}$ .

$x = \frac{\sqrt[7]{\sqrt[3]{2^{3}}}}{\sqrt[21]{9}}$

Step 5.2.4.2.3

Pull terms out from under the radical, assuming real numbers.

$x = \frac{\sqrt[7]{2}}{\sqrt[21]{9}}$

Step 6

The final solution is all the values that make $x (9 x^{21} - 8) = 0$ true.

$x = 0, \frac{\sqrt[7]{2}}{\sqrt[21]{9}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{\sqrt[7]{2}}{\sqrt[21]{9}}$

Decimal Form:

$x = 0, 0.99440698 \dots$