Solve k^40416-1 - ScanMath

Question

Simplify the expression

416 k^{4} - 1

Evaluate

k^{4} \times 416 - 1

Solution

416 k^{4} - 1

Show Solution

k_{1} = - \frac{4 17576}{52}, k_{2} = \frac{4 17576}{52}

Alternative Form

k_{1} \approx - 0.221425, k_{2} \approx 0.221425

Evaluate

k^{4} \times 416 - 1

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

k^{4} \times 416 - 1 = 0

Use the commutative property to reorder the terms

416 k^{4} - 1 = 0

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

416 k^{4} = 0 + 1

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

416 k^{4} = 1

Divide both sides

\frac{416 k ^{4}}{416} = \frac{1}{416}

Divide the numbers

k^{4} = \frac{1}{416}

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

k = \pm 4 \frac{1}{416}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{416}

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

\frac{4 1}{4 416}

Simplify the radical expression

\frac{1}{4 416}

Simplify the radical expression

More Steps

Evaluate

4416

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 26

Write the number in exponential form with the base of 2

4 2^{4} \times 26

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 426

Reduce the index of the radical and exponent with 4

2426

\frac{1}{2 4 26}

Multiply by the Conjugate

\frac{4 2 6 ^{3}}{2 4 26 \times 4 2 6 ^{3}}

Simplify

\frac{4 17576}{2 4 26 \times 4 2 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

2426 \times 4 2 6^{3}

Multiply the terms

2 \times 26

Multiply the terms

52

\frac{4 17576}{52}

k = \pm \frac{4 17576}{52}

Separate the equation into 2 possible cases

k = \frac{4 17576}{52} k = - \frac{4 17576}{52}

Solution

k_{1} = - \frac{4 17576}{52}, k_{2} = \frac{4 17576}{52}

Alternative Form

k_{1} \approx - 0.221425, k_{2} \approx 0.221425

Show Solution