Solve n^45678-1 - ScanMath

Question

Simplify the expression

5678 n^{4} - 1

Evaluate

n^{4} \times 5678 - 1

Solution

5678 n^{4} - 1

Show Solution

n_{1} = - \frac{4 567 8 ^{3}}{5678}, n_{2} = \frac{4 567 8 ^{3}}{5678}

Alternative Form

n_{1} \approx - 0.1152, n_{2} \approx 0.1152

Evaluate

n^{4} \times 5678 - 1

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

n^{4} \times 5678 - 1 = 0

Use the commutative property to reorder the terms

5678 n^{4} - 1 = 0

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

5678 n^{4} = 0 + 1

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

5678 n^{4} = 1

Divide both sides

\frac{5678 n ^{4}}{5678} = \frac{1}{5678}

Divide the numbers

n^{4} = \frac{1}{5678}

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

n = \pm 4 \frac{1}{5678}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{5678}

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

\frac{4 1}{4 5678}

Simplify the radical expression

\frac{1}{4 5678}

Multiply by the Conjugate

\frac{4 567 8 ^{3}}{4 5678 \times 4 567 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

45678 \times 4 567 8^{3}

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

4 5678 \times 567 8^{3}

Calculate the product

4 567 8^{4}

Reduce the index of the radical and exponent with 4

5678

\frac{4 567 8 ^{3}}{5678}

n = \pm \frac{4 567 8 ^{3}}{5678}

Separate the equation into 2 possible cases

n = \frac{4 567 8 ^{3}}{5678} n = - \frac{4 567 8 ^{3}}{5678}

Solution

n_{1} = - \frac{4 567 8 ^{3}}{5678}, n_{2} = \frac{4 567 8 ^{3}}{5678}

Alternative Form

n_{1} \approx - 0.1152, n_{2} \approx 0.1152

Show Solution