Solve p^41524-1 - Socratic AI (ScanMath)

Question

Simplify the expression

1524 p^{4} - 1

Evaluate

p^{4} \times 1524 - 1

Solution

1524 p^{4} - 1

Show Solution

p_{1} = - \frac{4 152 4 ^{3}}{1524}, p_{2} = \frac{4 152 4 ^{3}}{1524}

Alternative Form

p_{1} \approx - 0.160049, p_{2} \approx 0.160049

Evaluate

p^{4} \times 1524 - 1

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

p^{4} \times 1524 - 1 = 0

Use the commutative property to reorder the terms

1524 p^{4} - 1 = 0

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

1524 p^{4} = 0 + 1

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

1524 p^{4} = 1

Divide both sides

\frac{1524 p ^{4}}{1524} = \frac{1}{1524}

Divide the numbers

p^{4} = \frac{1}{1524}

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

p = \pm 4 \frac{1}{1524}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{1524}

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

\frac{4 1}{4 1524}

Simplify the radical expression

\frac{1}{4 1524}

Multiply by the Conjugate

\frac{4 152 4 ^{3}}{4 1524 \times 4 152 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

41524 \times 4 152 4^{3}

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

4 1524 \times 152 4^{3}

Calculate the product

4 152 4^{4}

Reduce the index of the radical and exponent with 4

1524

\frac{4 152 4 ^{3}}{1524}

p = \pm \frac{4 152 4 ^{3}}{1524}

Separate the equation into 2 possible cases

p = \frac{4 152 4 ^{3}}{1524} p = - \frac{4 152 4 ^{3}}{1524}

Solution

p_{1} = - \frac{4 152 4 ^{3}}{1524}, p_{2} = \frac{4 152 4 ^{3}}{1524}

Alternative Form

p_{1} \approx - 0.160049, p_{2} \approx 0.160049

Show Solution