Solve 22206-e/c^3

Question

Simplify the expression

\frac{22206 c ^{3} - e}{c ^{3}}

Evaluate

22206 - \frac{e}{c ^{3}}

Reduce fractions to a common denominator

\frac{22206 c ^{3}}{c ^{3}} - \frac{e}{c ^{3}}

Solution

\frac{22206 c ^{3} - e}{c ^{3}}

Show Solution

c = 0

Evaluate

22206 - \frac{e}{c ^{3}}

To find the excluded values,set the denominators equal to 0

c^{3} = 0

Solution

c = 0

Show Solution

c = \frac{3 2220 6 ^{2} e}{22206}

Alternative Form

c \approx 0.049653

Evaluate

22206 - \frac{e}{c ^{3}}

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

22206 - \frac{e}{c ^{3}} = 0

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

22206 - \frac{e}{c ^{3}} = 0, c \neq = 0

Calculate

22206 - \frac{e}{c ^{3}} = 0

Subtract the terms

More Steps

Simplify

22206 - \frac{e}{c ^{3}}

Reduce fractions to a common denominator

\frac{22206 c ^{3}}{c ^{3}} - \frac{e}{c ^{3}}

Write all numerators above the common denominator

\frac{22206 c ^{3} - e}{c ^{3}}

\frac{22206 c ^{3} - e}{c ^{3}} = 0

Cross multiply

22206 c^{3} - e = c^{3} \times 0

Simplify the equation

22206 c^{3} - e = 0

Move the constant to the right side

22206 c^{3} = e

Divide both sides

\frac{22206 c ^{3}}{22206} = \frac{e}{22206}

Divide the numbers

c^{3} = \frac{e}{22206}

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

3 c^{3} = 3 \frac{e}{22206}

Calculate

c = 3 \frac{e}{22206}

Simplify the root

More Steps

Evaluate

3 \frac{e}{22206}

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

\frac{3 e}{3 22206}

Multiply by the Conjugate

\frac{3 e \times 3 2220 6 ^{2}}{3 22206 \times 3 2220 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

3 e \times 3 2220 6^{2}

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

3 e \times 2220 6^{2}

Calculate the product

3 2220 6^{2} e

\frac{3 2220 6 ^{2} e}{3 22206 \times 3 2220 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

322206 \times 3 2220 6^{2}

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

3 22206 \times 2220 6^{2}

Calculate the product

3 2220 6^{3}

Reduce the index of the radical and exponent with 3

22206

\frac{3 2220 6 ^{2} e}{22206}

c = \frac{3 2220 6 ^{2} e}{22206}

Check if the solution is in the defined range

c = \frac{3 2220 6 ^{2} e}{22206}, c \neq = 0

Solution

c = \frac{3 2220 6 ^{2} e}{22206}

Alternative Form

c \approx 0.049653

Show Solution