Algebra Examples

$12 m \cdot 4 \cdot m = 48$

Step 1

Simplify.

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Step 1.1

Multiply $4$ by $12$ .

$48 m \cdot m = 48$

Step 1.2

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

$48 (m^{1} m) = 48$

Step 1.3

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

$48 (m^{1} m^{1}) = 48$

Step 1.4

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

$48 m^{1 + 1} = 48$

Step 1.5

Add $1$ and $1$ .

$48 m^{2} = 48$

Step 2

Divide each term in $48 m^{2} = 48$ by $48$ and simplify.

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Step 2.1

Divide each term in $48 m^{2} = 48$ by $48$ .

$\frac{48 m^{2}}{48} = \frac{48}{48}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $48$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{48 m^{2}}{48} = \frac{48}{48}$

Step 2.2.1.2

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

$m^{2} = \frac{48}{48}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $48$ by $48$ .

$m^{2} = 1$

Step 3

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

$m = \pm \sqrt{1}$

Step 4

Any root of $1$ is $1$ .

$m = \pm 1$

Step 5

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

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Step 5.1

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

$m = 1$

Step 5.2

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

$m = - 1$

Step 5.3

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

$m = 1, - 1$