Solve p^41538-1 - ScanMath

Question

Simplify the expression

1538 p^{4} - 1

Evaluate

p^{4} \times 1538 - 1

Solution

1538 p^{4} - 1

Show Solution

p_{1} = - \frac{4 153 8 ^{3}}{1538}, p_{2} = \frac{4 153 8 ^{3}}{1538}

Alternative Form

p_{1} \approx - 0.159684, p_{2} \approx 0.159684

Evaluate

p^{4} \times 1538 - 1

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

p^{4} \times 1538 - 1 = 0

Use the commutative property to reorder the terms

1538 p^{4} - 1 = 0

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

1538 p^{4} = 0 + 1

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

1538 p^{4} = 1

Divide both sides

\frac{1538 p ^{4}}{1538} = \frac{1}{1538}

Divide the numbers

p^{4} = \frac{1}{1538}

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

p = \pm 4 \frac{1}{1538}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1538}

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

\frac{4 1}{4 1538}

Simplify the radical expression

\frac{1}{4 1538}

Multiply by the Conjugate

\frac{4 153 8 ^{3}}{4 1538 \times 4 153 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

41538 \times 4 153 8^{3}

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

4 1538 \times 153 8^{3}

Calculate the product

4 153 8^{4}

Reduce the index of the radical and exponent with 4

1538

\frac{4 153 8 ^{3}}{1538}

p = \pm \frac{4 153 8 ^{3}}{1538}

Separate the equation into 2 possible cases

p = \frac{4 153 8 ^{3}}{1538} p = - \frac{4 153 8 ^{3}}{1538}

Solution

p_{1} = - \frac{4 153 8 ^{3}}{1538}, p_{2} = \frac{4 153 8 ^{3}}{1538}

Alternative Form

p_{1} \approx - 0.159684, p_{2} \approx 0.159684

Show Solution