Solve n^41010-1 - ScanMath

Question

Simplify the expression

1010 n^{4} - 1

Evaluate

n^{4} \times 1010 - 1

Solution

1010 n^{4} - 1

Show Solution

n_{1} = - \frac{4 101 0 ^{3}}{1010}, n_{2} = \frac{4 101 0 ^{3}}{1010}

Alternative Form

n_{1} \approx - 0.177386, n_{2} \approx 0.177386

Evaluate

n^{4} \times 1010 - 1

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

n^{4} \times 1010 - 1 = 0

Use the commutative property to reorder the terms

1010 n^{4} - 1 = 0

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

1010 n^{4} = 0 + 1

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

1010 n^{4} = 1

Divide both sides

\frac{1010 n ^{4}}{1010} = \frac{1}{1010}

Divide the numbers

n^{4} = \frac{1}{1010}

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

n = \pm 4 \frac{1}{1010}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1010}

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

\frac{4 1}{4 1010}

Simplify the radical expression

\frac{1}{4 1010}

Multiply by the Conjugate

\frac{4 101 0 ^{3}}{4 1010 \times 4 101 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

41010 \times 4 101 0^{3}

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

4 1010 \times 101 0^{3}

Calculate the product

4 101 0^{4}

Reduce the index of the radical and exponent with 4

1010

\frac{4 101 0 ^{3}}{1010}

n = \pm \frac{4 101 0 ^{3}}{1010}

Separate the equation into 2 possible cases

n = \frac{4 101 0 ^{3}}{1010} n = - \frac{4 101 0 ^{3}}{1010}

Solution

n_{1} = - \frac{4 101 0 ^{3}}{1010}, n_{2} = \frac{4 101 0 ^{3}}{1010}

Alternative Form

n_{1} \approx - 0.177386, n_{2} \approx 0.177386

Show Solution