Solve k^632-50201

Question

Simplify the expression

32 k^{6} - 50201

Evaluate

k^{6} \times 32 - 50201

Solution

32 k^{6} - 50201

Show Solution

k_{1} = - \frac{6 100402}{2}, k_{2} = \frac{6 100402}{2}

Alternative Form

k_{1} \approx - 3.408739, k_{2} \approx 3.408739

Evaluate

k^{6} \times 32 - 50201

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

k^{6} \times 32 - 50201 = 0

Use the commutative property to reorder the terms

32 k^{6} - 50201 = 0

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

32 k^{6} = 0 + 50201

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

32 k^{6} = 50201

Divide both sides

\frac{32 k ^{6}}{32} = \frac{50201}{32}

Divide the numbers

k^{6} = \frac{50201}{32}

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

k = \pm 6 \frac{50201}{32}

Simplify the expression

More Steps

Evaluate

6 \frac{50201}{32}

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

\frac{6 50201}{6 32}

Multiply by the Conjugate

\frac{6 50201 \times 6 3 2 ^{5}}{6 32 \times 6 3 2 ^{5}}

Simplify

\frac{6 50201 \times 2 ^{4} 6 2}{6 32 \times 6 3 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

650201 \times 2^{4} 62

Multiply the terms

6100402 \times 2^{4}

Use the commutative property to reorder the terms

2^{4} 6100402

\frac{2 ^{4} 6 100402}{6 32 \times 6 3 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

632 \times 6 3 2^{5}

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

6 32 \times 3 2^{5}

Calculate the product

6 3 2^{6}

Transform the expression

6 2^{30}

Reduce the index of the radical and exponent with 6

2^{5}

\frac{2 ^{4} 6 100402}{2 ^{5}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{4}}{2 ^{5}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{5 - 4}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{6 100402}{2}

k = \pm \frac{6 100402}{2}

Separate the equation into 2 possible cases

k = \frac{6 100402}{2} k = - \frac{6 100402}{2}

Solution

k_{1} = - \frac{6 100402}{2}, k_{2} = \frac{6 100402}{2}

Alternative Form

k_{1} \approx - 3.408739, k_{2} \approx 3.408739

Show Solution