Algebra Examples

$\frac{3 x^{4}}{5 y^{3}} \div \frac{12 y^{- 4}}{5 x^{- 7}}$

Step 1

Set the denominator in $\frac{3 x^{4}}{5 y^{3}}$ equal to $0$ to find where the expression is undefined.

$5 y^{3} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Divide each term in $5 y^{3} = 0$ by $5$ and simplify.

Tap for more steps...

Step 2.1.1

Divide each term in $5 y^{3} = 0$ by $5$ .

$\frac{5 y^{3}}{5} = \frac{0}{5}$

Step 2.1.2

Simplify the left side.

Tap for more steps...

Step 2.1.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.2.1.1

Cancel the common factor.

$\frac{5 y^{3}}{5} = \frac{0}{5}$

Step 2.1.2.1.2

Divide $y^{3}$ by $1$ .

$y^{3} = \frac{0}{5}$

Step 2.1.3

Simplify the right side.

Tap for more steps...

Step 2.1.3.1

Divide $0$ by $5$ .

$y^{3} = 0$

Step 2.2

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

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

Step 2.3

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

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

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

$y = 0$

Step 3

Set the denominator in $\frac{12 y^{- 4}}{5 x^{- 7}}$ equal to $0$ to find where the expression is undefined.

$5 x^{- 7} = 0$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Simplify $5 x^{- 7}$ .

Tap for more steps...

Step 4.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$5 \frac{1}{x^{7}} = 0$

Step 4.1.2

Combine $5$ and $\frac{1}{x^{7}}$ .

$\frac{5}{x^{7}} = 0$

Step 4.2

Set the numerator equal to zero.

$5 = 0$

Step 4.3

Since $5 \neq 0$ , there are no solutions.

No solution

Step 5

Set the denominator in $\frac{3 x^{4}}{5 y^{3}} \div \frac{12 y^{- 4}}{5 x^{- 7}}$ equal to $0$ to find where the expression is undefined.

$\frac{12 y^{- 4}}{5 x^{- 7}} = 0$

Step 6

Solve for $x$ .

Tap for more steps...

Step 6.1

Set the numerator equal to zero.

$12 y^{- 4} = 0$

Step 6.2

Solve the equation for $x$ .

Tap for more steps...

Step 6.2.1

Simplify $12 y^{- 4}$ .

Tap for more steps...

Step 6.2.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$12 \frac{1}{y^{4}} = 0$

Step 6.2.1.2

Combine $12$ and $\frac{1}{y^{4}}$ .

$\frac{12}{y^{4}} = 0$

Step 6.2.2

Set the numerator equal to zero.

$12 = 0$

Step 6.2.3

Since $12 \neq 0$ , there are no solutions.

No solution

Step 7

Set the base in $y^{- 4}$ equal to $0$ to find where the expression is undefined.

$y = 0$

Step 8

Set the base in $x^{- 7}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 9