Solve 3v^2-v^5v^4v^2

Question

Simplify the expression

3 v^{2} - v^{11}

Evaluate

3 v^{2} - v^{5} \times v^{4} \times v^{2}

Solution

More Steps

Evaluate

v^{5} \times v^{4} \times v^{2}

Multiply the terms with the same base by adding their exponents

v^{5 + 4 + 2}

Add the numbers

v^{11}

3 v^{2} - v^{11}

Show Solution

v^{2} (3 - v^{9})

Evaluate

3 v^{2} - v^{5} \times v^{4} \times v^{2}

Multiply

More Steps

Evaluate

v^{5} \times v^{4} \times v^{2}

Multiply the terms with the same base by adding their exponents

v^{5 + 4 + 2}

Add the numbers

v^{11}

3 v^{2} - v^{11}

Rewrite the expression

v^{2} \times 3 - v^{2} \times v^{9}

Solution

v^{2} (3 - v^{9})

Show Solution

v_{1} = 0, v_{2} = 93

Alternative Form

v_{1} = 0, v_{2} \approx 1.129831

Evaluate

3 v^{2} - v^{5} \times v^{4} \times v^{2}

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

3 v^{2} - v^{5} \times v^{4} \times v^{2} = 0

Multiply

More Steps

Multiply the terms

v^{5} \times v^{4} \times v^{2}

Multiply the terms with the same base by adding their exponents

v^{5 + 4 + 2}

Add the numbers

v^{11}

3 v^{2} - v^{11} = 0

Factor the expression

v^{2} (3 - v^{9}) = 0

Separate the equation into 2 possible cases

v^{2} = 0 3 - v^{9} = 0

The only way a power can be 0 is when the base equals 0

v = 0 3 - v^{9} = 0

Solve the equation

More Steps

Evaluate

3 - v^{9} = 0

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

- v^{9} = 0 - 3

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

- v^{9} = - 3

Change the signs on both sides of the equation

v^{9} = 3

Take the 9 -th root on both sides of the equation

9 v^{9} = 93

Calculate

v = 93

v = 0 v = 93

Solution

v_{1} = 0, v_{2} = 93

Alternative Form

v_{1} = 0, v_{2} \approx 1.129831

Show Solution