Pre-Algebra Examples

$c^{3} x c = c^{5}$

Step 1

Multiply $c^{3}$ by $c$ by adding the exponents.

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Step 1.1

Move $c$ .

$c \cdot c^{3} x = c^{5}$

Step 1.2

Multiply $c$ by $c^{3}$ .

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Step 1.2.1

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

$c^{1} c^{3} x = c^{5}$

Step 1.2.2

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

$c^{1 + 3} x = c^{5}$

Step 1.3

Add $1$ and $3$ .

$c^{4} x = c^{5}$

Step 2

Subtract $c^{5}$ from both sides of the equation.

$c^{4} x - c^{5} = 0$

Step 3

Factor $c^{4}$ out of $c^{4} x - c^{5}$ .

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Step 3.1

Factor $c^{4}$ out of $c^{4} x$ .

$c^{4} (x) - c^{5} = 0$

Step 3.2

Factor $c^{4}$ out of $- c^{5}$ .

$c^{4} (x) + c^{4} (- c) = 0$

Step 3.3

Factor $c^{4}$ out of $c^{4} (x) + c^{4} (- c)$ .

$c^{4} (x - c) = 0$

Step 4

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

$c^{4} = 0$

$x - c = 0$

Step 5

Set $c^{4}$ equal to $0$ and solve for $c$ .

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Step 5.1

Set $c^{4}$ equal to $0$ .

$c^{4} = 0$

Step 5.2

Solve $c^{4} = 0$ for $c$ .

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Step 5.2.1

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

$c = \pm \sqrt[4]{0}$

Step 5.2.2

Simplify $\pm \sqrt[4]{0}$ .

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Step 5.2.2.1

Rewrite $0$ as $0^{4}$ .

$c = \pm \sqrt[4]{0^{4}}$

Step 5.2.2.2

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

$c = \pm 0$

Step 5.2.2.3

Plus or minus $0$ is $0$ .

$c = 0$

Step 6

Set $x - c$ equal to $0$ and solve for $c$ .

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Step 6.1

Set $x - c$ equal to $0$ .

$x - c = 0$

Step 6.2

Solve $x - c = 0$ for $c$ .

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Step 6.2.1

Subtract $x$ from both sides of the equation.

$- c = - x$

Step 6.2.2

Divide each term in $- c = - x$ by $- 1$ and simplify.

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Step 6.2.2.1

Divide each term in $- c = - x$ by $- 1$ .

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

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Dividing two negative values results in a positive value.

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

Step 6.2.2.2.2

Divide $c$ by $1$ .

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

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Dividing two negative values results in a positive value.

$c = \frac{x}{1}$

Step 6.2.2.3.2

Divide $x$ by $1$ .

$c = x$

Step 7

The final solution is all the values that make $c^{4} (x - c) = 0$ true.

$c = 0$

$c = x$