Solve p^41506-1 - ScanMath

Question

Simplify the expression

1506 p^{4} - 1

Evaluate

p^{4} \times 1506 - 1

Solution

1506 p^{4} - 1

Show Solution

p_{1} = - \frac{4 150 6 ^{3}}{1506}, p_{2} = \frac{4 150 6 ^{3}}{1506}

Alternative Form

p_{1} \approx - 0.160525, p_{2} \approx 0.160525

Evaluate

p^{4} \times 1506 - 1

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

p^{4} \times 1506 - 1 = 0

Use the commutative property to reorder the terms

1506 p^{4} - 1 = 0

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

1506 p^{4} = 0 + 1

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

1506 p^{4} = 1

Divide both sides

\frac{1506 p ^{4}}{1506} = \frac{1}{1506}

Divide the numbers

p^{4} = \frac{1}{1506}

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

p = \pm 4 \frac{1}{1506}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1506}

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

\frac{4 1}{4 1506}

Simplify the radical expression

\frac{1}{4 1506}

Multiply by the Conjugate

\frac{4 150 6 ^{3}}{4 1506 \times 4 150 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

41506 \times 4 150 6^{3}

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

4 1506 \times 150 6^{3}

Calculate the product

4 150 6^{4}

Reduce the index of the radical and exponent with 4

1506

\frac{4 150 6 ^{3}}{1506}

p = \pm \frac{4 150 6 ^{3}}{1506}

Separate the equation into 2 possible cases

p = \frac{4 150 6 ^{3}}{1506} p = - \frac{4 150 6 ^{3}}{1506}

Solution

p_{1} = - \frac{4 150 6 ^{3}}{1506}, p_{2} = \frac{4 150 6 ^{3}}{1506}

Alternative Form

p_{1} \approx - 0.160525, p_{2} \approx 0.160525

Show Solution