Solve p^64112-1 - ScanMath

Question

Simplify the expression

4112 p^{6} - 1

Evaluate

p^{6} \times 4112 - 1

Solution

4112 p^{6} - 1

Show Solution

p_{1} = - \frac{6 411 2 ^{5}}{4112}, p_{2} = \frac{6 411 2 ^{5}}{4112}

Alternative Form

p_{1} \approx - 0.249838, p_{2} \approx 0.249838

Evaluate

p^{6} \times 4112 - 1

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

p^{6} \times 4112 - 1 = 0

Use the commutative property to reorder the terms

4112 p^{6} - 1 = 0

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

4112 p^{6} = 0 + 1

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

4112 p^{6} = 1

Divide both sides

\frac{4112 p ^{6}}{4112} = \frac{1}{4112}

Divide the numbers

p^{6} = \frac{1}{4112}

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

p = \pm 6 \frac{1}{4112}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{4112}

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

\frac{6 1}{6 4112}

Simplify the radical expression

\frac{1}{6 4112}

Multiply by the Conjugate

\frac{6 411 2 ^{5}}{6 4112 \times 6 411 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

64112 \times 6 411 2^{5}

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

6 4112 \times 411 2^{5}

Calculate the product

6 411 2^{6}

Reduce the index of the radical and exponent with 6

4112

\frac{6 411 2 ^{5}}{4112}

p = \pm \frac{6 411 2 ^{5}}{4112}

Separate the equation into 2 possible cases

p = \frac{6 411 2 ^{5}}{4112} p = - \frac{6 411 2 ^{5}}{4112}

Solution

p_{1} = - \frac{6 411 2 ^{5}}{4112}, p_{2} = \frac{6 411 2 ^{5}}{4112}

Alternative Form

p_{1} \approx - 0.249838, p_{2} \approx 0.249838

Show Solution