Solve r^6801-8-0 - ScanMath

Question

r^{6} \times 801 - 8 - 0

Simplify the expression

801 r^{6} - 8

Evaluate

r^{6} \times 801 - 8 - 0

Use the commutative property to reorder the terms

801 r^{6} - 8 - 0

Solution

801 r^{6} - 8

Show Solution

r_{1} = - \frac{6 8 \times 80 1 ^{5}}{801}, r_{2} = \frac{6 8 \times 80 1 ^{5}}{801}

Alternative Form

r_{1} \approx - 0.464062, r_{2} \approx 0.464062

Evaluate

r^{6} \times 801 - 8 - 0

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

r^{6} \times 801 - 8 - 0 = 0

Use the commutative property to reorder the terms

801 r^{6} - 8 - 0 = 0

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

801 r^{6} - 8 = 0

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

801 r^{6} = 0 + 8

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

801 r^{6} = 8

Divide both sides

\frac{801 r ^{6}}{801} = \frac{8}{801}

Divide the numbers

r^{6} = \frac{8}{801}

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

r = \pm 6 \frac{8}{801}

Simplify the expression

More Steps

Evaluate

6 \frac{8}{801}

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

\frac{6 8}{6 801}

Simplify the radical expression

More Steps

Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{6 801}

Multiply by the Conjugate

\frac{2 \times 6 80 1 ^{5}}{6 801 \times 6 80 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

2 \times 6 80 1^{5}

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

6 2^{3} \times 6 80 1^{5}

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

6 2^{3} \times 80 1^{5}

Calculate the product

6 8 \times 80 1^{5}

\frac{6 8 \times 80 1 ^{5}}{6 801 \times 6 80 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

6801 \times 6 80 1^{5}

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

6 801 \times 80 1^{5}

Calculate the product

6 80 1^{6}

Reduce the index of the radical and exponent with 6

801

\frac{6 8 \times 80 1 ^{5}}{801}

r = \pm \frac{6 8 \times 80 1 ^{5}}{801}

Separate the equation into 2 possible cases

r = \frac{6 8 \times 80 1 ^{5}}{801} r = - \frac{6 8 \times 80 1 ^{5}}{801}

Solution

r_{1} = - \frac{6 8 \times 80 1 ^{5}}{801}, r_{2} = \frac{6 8 \times 80 1 ^{5}}{801}

Alternative Form

r_{1} \approx - 0.464062, r_{2} \approx 0.464062

Show Solution