Solve n^43568-1 - ScanMath

Question

Simplify the expression

3568 n^{4} - 1

Evaluate

n^{4} \times 3568 - 1

Solution

3568 n^{4} - 1

Show Solution

n_{1} = - \frac{4 22 3 ^{3}}{446}, n_{2} = \frac{4 22 3 ^{3}}{446}

Alternative Form

n_{1} \approx - 0.129388, n_{2} \approx 0.129388

Evaluate

n^{4} \times 3568 - 1

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

n^{4} \times 3568 - 1 = 0

Use the commutative property to reorder the terms

3568 n^{4} - 1 = 0

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

3568 n^{4} = 0 + 1

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

3568 n^{4} = 1

Divide both sides

\frac{3568 n ^{4}}{3568} = \frac{1}{3568}

Divide the numbers

n^{4} = \frac{1}{3568}

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

n = \pm 4 \frac{1}{3568}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{3568}

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

\frac{4 1}{4 3568}

Simplify the radical expression

\frac{1}{4 3568}

Simplify the radical expression

More Steps

Evaluate

43568

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

4 16 \times 223

Write the number in exponential form with the base of 2

4 2^{4} \times 223

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

4 2^{4} \times 4223

Reduce the index of the radical and exponent with 4

24223

\frac{1}{2 4 223}

Multiply by the Conjugate

\frac{4 22 3 ^{3}}{2 4 223 \times 4 22 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

24223 \times 4 22 3^{3}

Multiply the terms

2 \times 223

Multiply the terms

446

\frac{4 22 3 ^{3}}{446}

n = \pm \frac{4 22 3 ^{3}}{446}

Separate the equation into 2 possible cases

n = \frac{4 22 3 ^{3}}{446} n = - \frac{4 22 3 ^{3}}{446}

Solution

n_{1} = - \frac{4 22 3 ^{3}}{446}, n_{2} = \frac{4 22 3 ^{3}}{446}

Alternative Form

n_{1} \approx - 0.129388, n_{2} \approx 0.129388

Show Solution