Solve 9c^6002-4 - Socratic AI (ScanMath)

Question

Simplify the expression

18 c^{6} - 4

Evaluate

9 c^{6} \times 2 - 4

Solution

18 c^{6} - 4

Show Solution

2 (9 c^{6} - 2)

Evaluate

9 c^{6} \times 2 - 4

Multiply the terms

18 c^{6} - 4

Solution

2 (9 c^{6} - 2)

Show Solution

c_{1} = - \frac{6 162}{3}, c_{2} = \frac{6 162}{3}

Alternative Form

c_{1} \approx - 0.778272, c_{2} \approx 0.778272

Evaluate

9 c^{6} \times 2 - 4

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

9 c^{6} \times 2 - 4 = 0

Multiply the terms

18 c^{6} - 4 = 0

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

18 c^{6} = 0 + 4

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

18 c^{6} = 4

Divide both sides

\frac{18 c ^{6}}{18} = \frac{4}{18}

Divide the numbers

c^{6} = \frac{4}{18}

Cancel out the common factor 2

c^{6} = \frac{2}{9}

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

c = \pm 6 \frac{2}{9}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{9}

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

\frac{6 2}{6 9}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{6 2}{3 3}

Multiply by the Conjugate

\frac{6 2 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{6 2 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

62 \times 39

Use n a = mn a^{m} to expand the expression

62 \times 6 9^{2}

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

6 2 \times 9^{2}

Calculate the product

6162

\frac{6 162}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{6 162}{3}

c = \pm \frac{6 162}{3}

Separate the equation into 2 possible cases

c = \frac{6 162}{3} c = - \frac{6 162}{3}

Solution

c_{1} = - \frac{6 162}{3}, c_{2} = \frac{6 162}{3}

Alternative Form

c_{1} \approx - 0.778272, c_{2} \approx 0.778272

Show Solution