Precalculus Examples

$6908733 = \frac{3159}{r^{5}} r^{12}$

Step 1

Rewrite the equation as $\frac{3159}{r^{5}} \cdot r^{12} = 6908733$ .

$\frac{3159}{r^{5}} \cdot r^{12} = 6908733$

Step 2

Factor each term.

Tap for more steps...

Step 2.1

Combine $\frac{3159}{r^{5}}$ and $r^{12}$ .

$\frac{3159 r^{12}}{r^{5}} = 6908733$

Step 2.2

Reduce the expression $\frac{3159 r^{12}}{r^{5}}$ by cancelling the common factors.

Tap for more steps...

Step 2.2.1

Factor $r^{5}$ out of $3159 r^{12}$ .

$\frac{r^{5} (3159 r^{7})}{r^{5}} = 6908733$

Step 2.2.2

Multiply by $1$ .

$\frac{r^{5} (3159 r^{7})}{r^{5} \cdot 1} = 6908733$

Step 2.2.3

Cancel the common factor.

$\frac{r^{5} (3159 r^{7})}{r^{5} \cdot 1} = 6908733$

Step 2.2.4

Rewrite the expression.

$\frac{3159 r^{7}}{1} = 6908733$

Step 2.3

Divide $3159 r^{7}$ by $1$ .

$3159 r^{7} = 6908733$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Divide each term in $3159 r^{7} = 6908733$ by $3159$ and simplify.

Tap for more steps...

Step 3.1.1

Divide each term in $3159 r^{7} = 6908733$ by $3159$ .

$\frac{3159 r^{7}}{3159} = \frac{6908733}{3159}$

Step 3.1.2

Simplify the left side.

Tap for more steps...

Step 3.1.2.1

Cancel the common factor of $3159$ .

Tap for more steps...

Step 3.1.2.1.1

Cancel the common factor.

$\frac{3159 r^{7}}{3159} = \frac{6908733}{3159}$

Step 3.1.2.1.2

Divide $r^{7}$ by $1$ .

$r^{7} = \frac{6908733}{3159}$

Step 3.1.3

Simplify the right side.

Tap for more steps...

Step 3.1.3.1

Divide $6908733$ by $3159$ .

$r^{7} = 2187$

Step 3.2

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

$r = \sqrt[7]{2187}$

Step 3.3

Simplify $\sqrt[7]{2187}$ .

Tap for more steps...

Step 3.3.1

Rewrite $2187$ as $3^{7}$ .

$r = \sqrt[7]{3^{7}}$

Step 3.3.2

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

$r = 3$