Solve n^4 3n^3-54n^2

Question

Simplify the expression

3 n^{7} - 54 n^{2}

Evaluate

n^{4} \times 3 n^{3} - 54 n^{2}

Solution

More Steps

Evaluate

n^{4} \times 3 n^{3}

Multiply the terms with the same base by adding their exponents

n^{4 + 3} \times 3

Add the numbers

n^{7} \times 3

Use the commutative property to reorder the terms

3 n^{7}

3 n^{7} - 54 n^{2}

Show Solution

3 n^{2} (n^{5} - 18)

Evaluate

n^{4} \times 3 n^{3} - 54 n^{2}

Multiply

More Steps

Evaluate

n^{4} \times 3 n^{3}

Multiply the terms with the same base by adding their exponents

n^{4 + 3} \times 3

Add the numbers

n^{7} \times 3

Use the commutative property to reorder the terms

3 n^{7}

3 n^{7} - 54 n^{2}

Rewrite the expression

3 n^{2} \times n^{5} - 3 n^{2} \times 18

Solution

3 n^{2} (n^{5} - 18)

Show Solution

n_{1} = 0, n_{2} = 518

Alternative Form

n_{1} = 0, n_{2} \approx 1.782602

Evaluate

n^{4} \times 3 n^{3} - 54 n^{2}

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

n^{4} \times 3 n^{3} - 54 n^{2} = 0

Multiply

More Steps

Multiply the terms

n^{4} \times 3 n^{3}

Multiply the terms with the same base by adding their exponents

n^{4 + 3} \times 3

Add the numbers

n^{7} \times 3

Use the commutative property to reorder the terms

3 n^{7}

3 n^{7} - 54 n^{2} = 0

Factor the expression

3 n^{2} (n^{5} - 18) = 0

Divide both sides

n^{2} (n^{5} - 18) = 0

Separate the equation into 2 possible cases

n^{2} = 0 n^{5} - 18 = 0

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

n = 0 n^{5} - 18 = 0

Solve the equation

More Steps

Evaluate

n^{5} - 18 = 0

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

n^{5} = 0 + 18

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

n^{5} = 18

Take the 5 -th root on both sides of the equation

5 n^{5} = 518

Calculate

n = 518

n = 0 n = 518

Solution

n_{1} = 0, n_{2} = 518

Alternative Form

n_{1} = 0, n_{2} \approx 1.782602

Show Solution