Finite Math Examples

${(4 m)}^{3} = 1000$

Step 1

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

$4 m = \sqrt[3]{1000}$

Step 2

Divide each term in $4 m = \sqrt[3]{1000}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 m = \sqrt[3]{1000}$ by $4$ .

$\frac{4 m}{4} = \frac{\sqrt[3]{1000}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 m}{4} = \frac{\sqrt[3]{1000}}{4}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{\sqrt[3]{1000}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the numerator.

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Step 2.3.1.1

Rewrite $1000$ as $10^{3}$ .

$m = \frac{\sqrt[3]{10^{3}}}{4}$

Step 2.3.1.2

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

$m = \frac{10}{4}$

Step 2.3.2

Cancel the common factor of $10$ and $4$ .

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Step 2.3.2.1

Factor $2$ out of $10$ .

$m = \frac{2 (5)}{4}$

Step 2.3.2.2

Cancel the common factors.

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Step 2.3.2.2.1

Factor $2$ out of $4$ .

$m = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.3.2.2.2

Cancel the common factor.

$m = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.3.2.2.3

Rewrite the expression.

$m = \frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5}{2}$

Decimal Form:

$m = 2.5$

Mixed Number Form:

$m = 2 \frac{1}{2}$