Solve e^5-1620 v^3 v^4

Question

Simplify the expression

e^{5} - 1620 v^{7}

Evaluate

e^{5} - 1620 v^{3} \times v^{4}

Solution

More Steps

Evaluate

1620 v^{3} \times v^{4}

Multiply the terms with the same base by adding their exponents

1620 v^{3 + 4}

Add the numbers

1620 v^{7}

e^{5} - 1620 v^{7}

Show Solution

v = \frac{7 162 0 ^{6} e ^{5}}{1620}

Alternative Form

v \approx 0.710736

Evaluate

e^{5} - 1620 v^{3} \times v^{4}

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

e^{5} - 1620 v^{3} \times v^{4} = 0

Multiply

More Steps

Multiply the terms

1620 v^{3} \times v^{4}

Multiply the terms with the same base by adding their exponents

1620 v^{3 + 4}

Add the numbers

1620 v^{7}

e^{5} - 1620 v^{7} = 0

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

- 1620 v^{7} = 0 - e^{5}

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

- 1620 v^{7} = - e^{5}

Change the signs on both sides of the equation

1620 v^{7} = e^{5}

Divide both sides

\frac{1620 v ^{7}}{1620} = \frac{e ^{5}}{1620}

Divide the numbers

v^{7} = \frac{e ^{5}}{1620}

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

7 v^{7} = 7 \frac{e ^{5}}{1620}

Calculate

v = 7 \frac{e ^{5}}{1620}

Solution

More Steps

Evaluate

7 \frac{e ^{5}}{1620}

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

\frac{7 e ^{5}}{7 1620}

Multiply by the Conjugate

\frac{7 e ^{5} \times 7 162 0 ^{6}}{7 1620 \times 7 162 0 ^{6}}

Multiply the numbers

More Steps

Evaluate

7 e^{5} \times 7 162 0^{6}

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

7 e^{5} \times 162 0^{6}

Calculate the product

7 162 0^{6} e^{5}

\frac{7 162 0 ^{6} e ^{5}}{7 1620 \times 7 162 0 ^{6}}

Multiply the numbers

More Steps

Evaluate

71620 \times 7 162 0^{6}

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

7 1620 \times 162 0^{6}

Calculate the product

7 162 0^{7}

Reduce the index of the radical and exponent with 7

1620

\frac{7 162 0 ^{6} e ^{5}}{1620}

v = \frac{7 162 0 ^{6} e ^{5}}{1620}

Alternative Form

v \approx 0.710736

Show Solution