Solve b^-3 - 5 - ScanMath

Question

Simplify the expression

\frac{1 - 5 b ^{3}}{b ^{3}}

Evaluate

b^{- 3} - 5

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

\frac{1}{b ^{3}} - 5

Reduce fractions to a common denominator

\frac{1}{b ^{3}} - \frac{5 b ^{3}}{b ^{3}}

Solution

\frac{1 - 5 b ^{3}}{b ^{3}}

Show Solution

b = \frac{3 25}{5}

Alternative Form

b \approx 0.584804

Evaluate

b^{- 3} - 5

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

b^{- 3} - 5 = 0

Find the domain

b^{- 3} - 5 = 0, b \neq = 0

Calculate

b^{- 3} - 5 = 0

Move the constant to the right-hand side and change its sign

b^{- 3} = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

b^{- 3} = 5

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

\frac{1}{b ^{3}} = 5

Cross multiply

1 = b^{3} \times 5

Simplify the equation

1 = 5 b^{3}

Swap the sides of the equation

5 b^{3} = 1

Divide both sides

\frac{5 b ^{3}}{5} = \frac{1}{5}

Divide the numbers

b^{3} = \frac{1}{5}

Take the 3 -th root on both sides of the equation

3 b^{3} = 3 \frac{1}{5}

Calculate

b = 3 \frac{1}{5}

Simplify the root

More Steps

Evaluate

3 \frac{1}{5}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 5}

Simplify the radical expression

\frac{1}{3 5}

Multiply by the Conjugate

\frac{3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

The product of roots with the same index is equal to the root of the product

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 25}{5}

b = \frac{3 25}{5}

Check if the solution is in the defined range

b = \frac{3 25}{5}, b \neq = 0

Solution

b = \frac{3 25}{5}

Alternative Form

b \approx 0.584804

Show Solution