Finite Math Examples

${(\frac{a^{3}}{5 m})}^{- 4}$

Step 1

Set the denominator in $\frac{a^{3}}{5 m}$ equal to $0$ to find where the expression is undefined.

$5 m = 0$

Step 2

Divide each term in $5 m = 0$ by $5$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $5 m = 0$ by $5$ .

$\frac{5 m}{5} = \frac{0}{5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{5 m}{5} = \frac{0}{5}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{0}{5}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $0$ by $5$ .

$m = 0$

Step 3

Set the base in ${(\frac{a^{3}}{5 m})}^{- 4}$ equal to $0$ to find where the expression is undefined.

$\frac{a^{3}}{5 m} = 0$

Step 4

Solve for $a$ .

Tap for more steps...

Step 4.1

Set the numerator equal to zero.

$a^{3} = 0$

Step 4.2

Solve the equation for $a$ .

Tap for more steps...

Step 4.2.1

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

$a = \sqrt[3]{0}$

Step 4.2.2

Simplify $\sqrt[3]{0}$ .

Tap for more steps...

Step 4.2.2.1

Rewrite $0$ as $0^{3}$ .

$a = \sqrt[3]{0^{3}}$

Step 4.2.2.2

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

$a = 0$

Step 5

The domain is all values of $a$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${a | a \neq 0}$