Solve (9n^3)(8n-1)(7n)

Question

Simplify the expression

504 n^{5} - 63 n^{4}

Evaluate

9 n^{3} (8 n - 1) \times 7 n

Multiply the terms

63 n^{3} (8 n - 1) n

Multiply the terms with the same base by adding their exponents

63 n^{3 + 1} (8 n - 1)

Add the numbers

63 n^{4} (8 n - 1)

Apply the distributive property

63 n^{4} \times 8 n - 63 n^{4} \times 1

Multiply the terms

More Steps

Evaluate

63 n^{4} \times 8 n

Multiply the numbers

504 n^{4} \times n

Multiply the terms

More Steps

Evaluate

n^{4} \times n

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

n^{4 + 1}

Add the numbers

n^{5}

504 n^{5}

504 n^{5} - 63 n^{4} \times 1

Solution

504 n^{5} - 63 n^{4}

Show Solution

n_{1} = 0, n_{2} = \frac{1}{8}

Alternative Form

n_{1} = 0, n_{2} = 0.125

Evaluate

(9 n^{3}) (8 n - 1) (7 n)

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

(9 n^{3}) (8 n - 1) (7 n) = 0

Multiply the terms

9 n^{3} (8 n - 1) (7 n) = 0

Multiply the terms

9 n^{3} (8 n - 1) \times 7 n = 0

Multiply

More Steps

Multiply the terms

9 n^{3} (8 n - 1) \times 7 n

Multiply the terms

63 n^{3} (8 n - 1) n

Multiply the terms with the same base by adding their exponents

63 n^{3 + 1} (8 n - 1)

Add the numbers

63 n^{4} (8 n - 1)

63 n^{4} (8 n - 1) = 0

Elimination the left coefficient

n^{4} (8 n - 1) = 0

Separate the equation into 2 possible cases

n^{4} = 0 8 n - 1 = 0

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

n = 0 8 n - 1 = 0

Solve the equation

More Steps

Evaluate

8 n - 1 = 0

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

8 n = 0 + 1

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

8 n = 1

Divide both sides

\frac{8 n}{8} = \frac{1}{8}

Divide the numbers

n = \frac{1}{8}

n = 0 n = \frac{1}{8}

Solution

n_{1} = 0, n_{2} = \frac{1}{8}

Alternative Form

n_{1} = 0, n_{2} = 0.125

Show Solution