Solve p^67644-1 - Socratic AI (ScanMath)

Question

Simplify the expression

7644 p^{6} - 1

Evaluate

p^{6} \times 7644 - 1

Solution

7644 p^{6} - 1

Show Solution

p_{1} = - \frac{6 764 4 ^{5}}{7644}, p_{2} = \frac{6 764 4 ^{5}}{7644}

Alternative Form

p_{1} \approx - 0.22531, p_{2} \approx 0.22531

Evaluate

p^{6} \times 7644 - 1

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

p^{6} \times 7644 - 1 = 0

Use the commutative property to reorder the terms

7644 p^{6} - 1 = 0

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

7644 p^{6} = 0 + 1

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

7644 p^{6} = 1

Divide both sides

\frac{7644 p ^{6}}{7644} = \frac{1}{7644}

Divide the numbers

p^{6} = \frac{1}{7644}

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

p = \pm 6 \frac{1}{7644}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{7644}

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

\frac{6 1}{6 7644}

Simplify the radical expression

\frac{1}{6 7644}

Multiply by the Conjugate

\frac{6 764 4 ^{5}}{6 7644 \times 6 764 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

67644 \times 6 764 4^{5}

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

6 7644 \times 764 4^{5}

Calculate the product

6 764 4^{6}

Reduce the index of the radical and exponent with 6

7644

\frac{6 764 4 ^{5}}{7644}

p = \pm \frac{6 764 4 ^{5}}{7644}

Separate the equation into 2 possible cases

p = \frac{6 764 4 ^{5}}{7644} p = - \frac{6 764 4 ^{5}}{7644}

Solution

p_{1} = - \frac{6 764 4 ^{5}}{7644}, p_{2} = \frac{6 764 4 ^{5}}{7644}

Alternative Form

p_{1} \approx - 0.22531, p_{2} \approx 0.22531

Show Solution