Solve f^30340i^20140-100

Question

Simplify the expression

- 47600 f^{3} - 100

Evaluate

f^{3} \times 340 i^{2} \times 140 - 100

Evaluate the power

f^{3} \times 340 (- 1) \times 140 - 100

Solution

More Steps

Multiply the terms

f^{3} \times 340 (- 1) \times 140

Any expression multiplied by 1 remains the same

- f^{3} \times 340 \times 140

Multiply the terms

- f^{3} \times 47600

Use the commutative property to reorder the terms

- 47600 f^{3}

- 47600 f^{3} - 100

Show Solution

Factor the expression

- 100 (476 f^{3} + 1)

Evaluate

f^{3} \times 340 i^{2} \times 140 - 100

Evaluate the power

f^{3} \times 340 (- 1) \times 140 - 100

Multiply

More Steps

Multiply the terms

f^{3} \times 340 (- 1) \times 140

Any expression multiplied by 1 remains the same

- f^{3} \times 340 \times 140

Multiply the terms

- f^{3} \times 47600

Use the commutative property to reorder the terms

- 47600 f^{3}

- 47600 f^{3} - 100

Solution

- 100 (476 f^{3} + 1)

Show Solution

Find the roots

f = - \frac{3 47 6 ^{2}}{476}

Alternative Form

f \approx - 0.128075

Evaluate

f^{3} \times 340 i^{2} \times 140 - 100

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

f^{3} \times 340 i^{2} \times 140 - 100 = 0

Evaluate the power

f^{3} \times 340 (- 1) \times 140 - 100 = 0

Multiply

More Steps

Multiply the terms

f^{3} \times 340 (- 1) \times 140

Any expression multiplied by 1 remains the same

- f^{3} \times 340 \times 140

Multiply the terms

- f^{3} \times 47600

Use the commutative property to reorder the terms

- 47600 f^{3}

- 47600 f^{3} - 100 = 0

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

- 47600 f^{3} = 0 + 100

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

- 47600 f^{3} = 100

Change the signs on both sides of the equation

47600 f^{3} = - 100

Divide both sides

\frac{47600 f ^{3}}{47600} = \frac{- 100}{47600}

Divide the numbers

f^{3} = \frac{- 100}{47600}

Divide the numbers

More Steps

Evaluate

\frac{- 100}{47600}

Cancel out the common factor 100

\frac{- 1}{476}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{476}

f^{3} = - \frac{1}{476}

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

3 f^{3} = 3 - \frac{1}{476}

Calculate

f = 3 - \frac{1}{476}

Solution

More Steps

Evaluate

3 - \frac{1}{476}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{476}

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

- \frac{3 1}{3 476}

Simplify the radical expression

- \frac{1}{3 476}

Multiply by the Conjugate

\frac{- 3 47 6 ^{2}}{3 476 \times 3 47 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

3476 \times 3 47 6^{2}

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

3 476 \times 47 6^{2}

Calculate the product

3 47 6^{3}

Reduce the index of the radical and exponent with 3

476

\frac{- 3 47 6 ^{2}}{476}

Calculate

- \frac{3 47 6 ^{2}}{476}

f = - \frac{3 47 6 ^{2}}{476}

Alternative Form

f \approx - 0.128075

Show Solution