Pre-Algebra Examples

$\frac{3 m^{7}}{m} = 2 m^{6}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{3 m^{7}}{m}$ by cancelling the common factors.

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Step 1.1.1

Factor $m$ out of $3 m^{7}$ .

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

Step 1.1.2

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

$\frac{m (3 m^{6})}{m^{1}} = 2 m^{6}$

Step 1.1.3

Factor $m$ out of $m^{1}$ .

$\frac{m (3 m^{6})}{m \cdot 1} = 2 m^{6}$

Step 1.1.4

Cancel the common factor.

$\frac{m (3 m^{6})}{m \cdot 1} = 2 m^{6}$

Step 1.1.5

Rewrite the expression.

$\frac{3 m^{6}}{1} = 2 m^{6}$

Step 1.2

Divide $3 m^{6}$ by $1$ .

$3 m^{6} = 2 m^{6}$

Step 2

Solve the equation.

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Step 2.1

Move all terms containing $m$ to the left side of the equation.

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Step 2.1.1

Subtract $2 m^{6}$ from both sides of the equation.

$3 m^{6} - 2 m^{6} = 0$

Step 2.1.2

Subtract $2 m^{6}$ from $3 m^{6}$ .

$m^{6} = 0$

Step 2.2

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

$m = \pm \sqrt[6]{0}$

Step 2.3

Simplify $\pm \sqrt[6]{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{6}$ .

$m = \pm \sqrt[6]{0^{6}}$

Step 2.3.2

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

$m = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$m = 0$

Step 3

Exclude the solutions that do not make $\frac{3 m^{7}}{m} = 2 m^{6}$ true.

$No solution$