Solve c^6320160-100

Question

Simplify the expression

320160 c^{6} - 100

Evaluate

c^{6} \times 320160 - 100

Solution

320160 c^{6} - 100

Show Solution

20 (16008 c^{6} - 5)

Evaluate

c^{6} \times 320160 - 100

Use the commutative property to reorder the terms

320160 c^{6} - 100

Solution

20 (16008 c^{6} - 5)

Show Solution

c_{1} = - \frac{6 5 \times 1600 8 ^{5}}{16008}, c_{2} = \frac{6 5 \times 1600 8 ^{5}}{16008}

Alternative Form

c_{1} \approx - 0.260479, c_{2} \approx 0.260479

Evaluate

c^{6} \times 320160 - 100

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

c^{6} \times 320160 - 100 = 0

Use the commutative property to reorder the terms

320160 c^{6} - 100 = 0

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

320160 c^{6} = 0 + 100

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

320160 c^{6} = 100

Divide both sides

\frac{320160 c ^{6}}{320160} = \frac{100}{320160}

Divide the numbers

c^{6} = \frac{100}{320160}

Cancel out the common factor 20

c^{6} = \frac{5}{16008}

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

c = \pm 6 \frac{5}{16008}

Simplify the expression

More Steps

Evaluate

6 \frac{5}{16008}

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

\frac{6 5}{6 16008}

Multiply by the Conjugate

\frac{6 5 \times 6 1600 8 ^{5}}{6 16008 \times 6 1600 8 ^{5}}

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

\frac{6 5 \times 1600 8 ^{5}}{6 16008 \times 6 1600 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

616008 \times 6 1600 8^{5}

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

6 16008 \times 1600 8^{5}

Calculate the product

6 1600 8^{6}

Reduce the index of the radical and exponent with 6

16008

\frac{6 5 \times 1600 8 ^{5}}{16008}

c = \pm \frac{6 5 \times 1600 8 ^{5}}{16008}

Separate the equation into 2 possible cases

c = \frac{6 5 \times 1600 8 ^{5}}{16008} c = - \frac{6 5 \times 1600 8 ^{5}}{16008}

Solution

c_{1} = - \frac{6 5 \times 1600 8 ^{5}}{16008}, c_{2} = \frac{6 5 \times 1600 8 ^{5}}{16008}

Alternative Form

c_{1} \approx - 0.260479, c_{2} \approx 0.260479

Show Solution