Solve p^43970-1 - Socratic AI (ScanMath)

Question

Simplify the expression

3970 p^{4} - 1

Evaluate

p^{4} \times 3970 - 1

Solution

3970 p^{4} - 1

Show Solution

p_{1} = - \frac{4 397 0 ^{3}}{3970}, p_{2} = \frac{4 397 0 ^{3}}{3970}

Alternative Form

p_{1} \approx - 0.12598, p_{2} \approx 0.12598

Evaluate

p^{4} \times 3970 - 1

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

p^{4} \times 3970 - 1 = 0

Use the commutative property to reorder the terms

3970 p^{4} - 1 = 0

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

3970 p^{4} = 0 + 1

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

3970 p^{4} = 1

Divide both sides

\frac{3970 p ^{4}}{3970} = \frac{1}{3970}

Divide the numbers

p^{4} = \frac{1}{3970}

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

p = \pm 4 \frac{1}{3970}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{3970}

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

\frac{4 1}{4 3970}

Simplify the radical expression

\frac{1}{4 3970}

Multiply by the Conjugate

\frac{4 397 0 ^{3}}{4 3970 \times 4 397 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

43970 \times 4 397 0^{3}

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

4 3970 \times 397 0^{3}

Calculate the product

4 397 0^{4}

Reduce the index of the radical and exponent with 4

3970

\frac{4 397 0 ^{3}}{3970}

p = \pm \frac{4 397 0 ^{3}}{3970}

Separate the equation into 2 possible cases

p = \frac{4 397 0 ^{3}}{3970} p = - \frac{4 397 0 ^{3}}{3970}

Solution

p_{1} = - \frac{4 397 0 ^{3}}{3970}, p_{2} = \frac{4 397 0 ^{3}}{3970}

Alternative Form

p_{1} \approx - 0.12598, p_{2} \approx 0.12598

Show Solution