Solve e^5-2620 v^3 e^5620

Question

Simplify the expression

e^{5} - 1624400 e^{5} v^{3}

Evaluate

e^{5} - 2620 v^{3} e^{5} \times 620

Solution

More Steps

Evaluate

2620 v^{3} e^{5} \times 620

Multiply the terms

1624400 v^{3} e^{5}

Multiply the numbers

1624400 e^{5} v^{3}

e^{5} - 1624400 e^{5} v^{3}

Show Solution

Factor the expression

e^{5} (1 - 1624400 v^{3})

Evaluate

e^{5} - 2620 v^{3} e^{5} \times 620

Multiply

More Steps

Evaluate

2620 v^{3} e^{5} \times 620

Multiply the terms

1624400 v^{3} e^{5}

Multiply the numbers

1624400 e^{5} v^{3}

e^{5} - 1624400 e^{5} v^{3}

Solution

e^{5} (1 - 1624400 v^{3})

Show Solution

Find the roots

v = \frac{3 20305 0 ^{2}}{406100}

Alternative Form

v \approx 0.008507

Evaluate

e^{5} - 2620 v^{3} e^{5} \times 620

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

e^{5} - 2620 v^{3} e^{5} \times 620 = 0

Multiply

More Steps

Multiply the terms

2620 v^{3} e^{5} \times 620

Multiply the terms

1624400 v^{3} e^{5}

Multiply the numbers

1624400 e^{5} v^{3}

e^{5} - 1624400 e^{5} v^{3} = 0

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

- 1624400 e^{5} v^{3} = 0 - e^{5}

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

- 1624400 e^{5} v^{3} = - e^{5}

Change the signs on both sides of the equation

1624400 e^{5} v^{3} = e^{5}

Divide both sides

\frac{1624400 e ^{5} v ^{3}}{1624400 e ^{5}} = \frac{e ^{5}}{1624400 e ^{5}}

Divide the numbers

v^{3} = \frac{e ^{5}}{1624400 e ^{5}}

Divide the numbers

v^{3} = \frac{1}{1624400}

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

3 v^{3} = 3 \frac{1}{1624400}

Calculate

v = 3 \frac{1}{1624400}

Solution

More Steps

Evaluate

3 \frac{1}{1624400}

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

\frac{3 1}{3 1624400}

Simplify the radical expression

\frac{1}{3 1624400}

Simplify the radical expression

More Steps

Evaluate

31624400

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 203050

Write the number in exponential form with the base of 2

3 2^{3} \times 203050

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 3203050

Reduce the index of the radical and exponent with 3

23203050

\frac{1}{2 3 203050}

Multiply by the Conjugate

\frac{3 20305 0 ^{2}}{2 3 203050 \times 3 20305 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

23203050 \times 3 20305 0^{2}

Multiply the terms

2 \times 203050

Multiply the terms

406100

\frac{3 20305 0 ^{2}}{406100}

v = \frac{3 20305 0 ^{2}}{406100}

Alternative Form

v \approx 0.008507

Show Solution