Solve (-3b^430b^210b-6)/(b^3)

Question

Simplify the expression

- \frac{900 b ^{7} + 6}{b ^{3}}

Show Solution

b = 0

Show Solution

b = - \frac{7 15 0 ^{6}}{150}

Alternative Form

b \approx - 0.488798

Evaluate

\frac{- 3 b ^{4} \times 30 b ^{2} \times 10 b - 6}{b ^{3}}

To find the roots of the expression,set the expression equal to 0

\frac{- 3 b ^{4} \times 30 b ^{2} \times 10 b - 6}{b ^{3}} = 0

The only way a power can not be 0 is when the base not equals 0

\frac{- 3 b ^{4} \times 30 b ^{2} \times 10 b - 6}{b ^{3}} = 0, b \neq = 0

Calculate

\frac{- 3 b ^{4} \times 30 b ^{2} \times 10 b - 6}{b ^{3}} = 0

Multiply

More Steps

\frac{- 900 b ^{7} - 6}{b ^{3}} = 0

Cross multiply

- 900 b^{7} - 6 = b^{3} \times 0

Simplify the equation

- 900 b^{7} - 6 = 0

Move the constant to the right side

- 900 b^{7} = 6

Change the signs on both sides of the equation

900 b^{7} = - 6

Divide both sides

\frac{900 b ^{7}}{900} = \frac{- 6}{900}

Divide the numbers

b^{7} = \frac{- 6}{900}

Divide the numbers

More Steps

b^{7} = - \frac{1}{150}

Take the 7 -th root on both sides of the equation

7 b^{7} = 7 - \frac{1}{150}

Calculate

b = 7 - \frac{1}{150}

Simplify the root

More Steps

b = - \frac{7 15 0 ^{6}}{150}

Check if the solution is in the defined range

b = - \frac{7 15 0 ^{6}}{150}, b \neq = 0

Solution

b = - \frac{7 15 0 ^{6}}{150}

Alternative Form

b \approx - 0.488798

Show Solution