Solve S^652010-1/4

Question

Simplify the expression

52010 S^{6} - \frac{1}{4}

Evaluate

S^{6} \times 52010 - \frac{1}{4}

Solution

52010 S^{6} - \frac{1}{4}

Show Solution

\frac{1}{4} (208040 S^{6} - 1)

Evaluate

S^{6} \times 52010 - \frac{1}{4}

Use the commutative property to reorder the terms

52010 S^{6} - \frac{1}{4}

Solution

\frac{1}{4} (208040 S^{6} - 1)

Show Solution

S_{1} = - \frac{6 20804 0 ^{5}}{208040}, S_{2} = \frac{6 20804 0 ^{5}}{208040}

Alternative Form

S_{1} \approx - 0.12991, S_{2} \approx 0.12991

Evaluate

S^{6} \times 52010 - \frac{1}{4}

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

S^{6} \times 52010 - \frac{1}{4} = 0

Use the commutative property to reorder the terms

52010 S^{6} - \frac{1}{4} = 0

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

52010 S^{6} = 0 + \frac{1}{4}

Add the terms

52010 S^{6} = \frac{1}{4}

Multiply by the reciprocal

52010 S^{6} \times \frac{1}{52010} = \frac{1}{4} \times \frac{1}{52010}

Multiply

S^{6} = \frac{1}{4} \times \frac{1}{52010}

Multiply

More Steps

Evaluate

\frac{1}{4} \times \frac{1}{52010}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{4 \times 52010}

Multiply the numbers

\frac{1}{208040}

S^{6} = \frac{1}{208040}

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

S = \pm 6 \frac{1}{208040}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{208040}

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

\frac{6 1}{6 208040}

Simplify the radical expression

\frac{1}{6 208040}

Multiply by the Conjugate

\frac{6 20804 0 ^{5}}{6 208040 \times 6 20804 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

6208040 \times 6 20804 0^{5}

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

6 208040 \times 20804 0^{5}

Calculate the product

6 20804 0^{6}

Reduce the index of the radical and exponent with 6

208040

\frac{6 20804 0 ^{5}}{208040}

S = \pm \frac{6 20804 0 ^{5}}{208040}

Separate the equation into 2 possible cases

S = \frac{6 20804 0 ^{5}}{208040} S = - \frac{6 20804 0 ^{5}}{208040}

Solution

S_{1} = - \frac{6 20804 0 ^{5}}{208040}, S_{2} = \frac{6 20804 0 ^{5}}{208040}

Alternative Form

S_{1} \approx - 0.12991, S_{2} \approx 0.12991

Show Solution