Solve 8k^(3) 12k^(2) 6k-999

Question

Simplify the expression

576 k^{6} - 999

Evaluate

8 k^{3} \times 12 k^{2} \times 6 k - 999

Solution

More Steps

Evaluate

8 k^{3} \times 12 k^{2} \times 6 k

Multiply the terms

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Evaluate

8 \times 12 \times 6

Multiply the terms

96 \times 6

Multiply the numbers

576

576 k^{3} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

576 k^{3 + 2 + 1}

Add the numbers

576 k^{6}

576 k^{6} - 999

Show Solution

Factor the expression

9 (64 k^{6} - 111)

Evaluate

8 k^{3} \times 12 k^{2} \times 6 k - 999

Multiply

More Steps

Evaluate

8 k^{3} \times 12 k^{2} \times 6 k

Multiply the terms

More Steps

Evaluate

8 \times 12 \times 6

Multiply the terms

96 \times 6

Multiply the numbers

576

576 k^{3} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

576 k^{3 + 2 + 1}

Add the numbers

576 k^{6}

576 k^{6} - 999

Solution

9 (64 k^{6} - 111)

Show Solution

Find the roots

k_{1} = - \frac{6 111}{2}, k_{2} = \frac{6 111}{2}

Alternative Form

k_{1} \approx - 1.096118, k_{2} \approx 1.096118

Evaluate

8 k^{3} \times 12 k^{2} \times 6 k - 999

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

8 k^{3} \times 12 k^{2} \times 6 k - 999 = 0

Multiply

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Multiply the terms

8 k^{3} \times 12 k^{2} \times 6 k

Multiply the terms

More Steps

Evaluate

8 \times 12 \times 6

Multiply the terms

96 \times 6

Multiply the numbers

576

576 k^{3} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

576 k^{3 + 2 + 1}

Add the numbers

576 k^{6}

576 k^{6} - 999 = 0

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

576 k^{6} = 0 + 999

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

576 k^{6} = 999

Divide both sides

\frac{576 k ^{6}}{576} = \frac{999}{576}

Divide the numbers

k^{6} = \frac{999}{576}

Cancel out the common factor 9

k^{6} = \frac{111}{64}

Take the root of both sides of the equation and remember to use both positive and negative roots

k = \pm 6 \frac{111}{64}

Simplify the expression

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Evaluate

6 \frac{111}{64}

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

\frac{6 111}{6 64}

Simplify the radical expression

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Evaluate

664

Write the number in exponential form with the base of 2

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 111}{2}

k = \pm \frac{6 111}{2}

Separate the equation into 2 possible cases

k = \frac{6 111}{2} k = - \frac{6 111}{2}

Solution

k_{1} = - \frac{6 111}{2}, k_{2} = \frac{6 111}{2}

Alternative Form

k_{1} \approx - 1.096118, k_{2} \approx 1.096118

Show Solution