Solve h^41001-1 - ScanMath

Question

Simplify the expression

1001 h^{4} - 1

Evaluate

h^{4} \times 1001 - 1

Solution

1001 h^{4} - 1

Show Solution

h_{1} = - \frac{4 100 1 ^{3}}{1001}, h_{2} = \frac{4 100 1 ^{3}}{1001}

Alternative Form

h_{1} \approx - 0.177784, h_{2} \approx 0.177784

Evaluate

h^{4} \times 1001 - 1

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

h^{4} \times 1001 - 1 = 0

Use the commutative property to reorder the terms

1001 h^{4} - 1 = 0

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

1001 h^{4} = 0 + 1

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

1001 h^{4} = 1

Divide both sides

\frac{1001 h ^{4}}{1001} = \frac{1}{1001}

Divide the numbers

h^{4} = \frac{1}{1001}

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

h = \pm 4 \frac{1}{1001}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1001}

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

\frac{4 1}{4 1001}

Simplify the radical expression

\frac{1}{4 1001}

Multiply by the Conjugate

\frac{4 100 1 ^{3}}{4 1001 \times 4 100 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

41001 \times 4 100 1^{3}

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

4 1001 \times 100 1^{3}

Calculate the product

4 100 1^{4}

Reduce the index of the radical and exponent with 4

1001

\frac{4 100 1 ^{3}}{1001}

h = \pm \frac{4 100 1 ^{3}}{1001}

Separate the equation into 2 possible cases

h = \frac{4 100 1 ^{3}}{1001} h = - \frac{4 100 1 ^{3}}{1001}

Solution

h_{1} = - \frac{4 100 1 ^{3}}{1001}, h_{2} = \frac{4 100 1 ^{3}}{1001}

Alternative Form

h_{1} \approx - 0.177784, h_{2} \approx 0.177784

Show Solution