Solve p^48222-1 - ScanMath

Question

Simplify the expression

Solution

8222 p^{4} - 1

Evaluate

p^{4} \times 8222 - 1

Solution

8222 p^{4} - 1

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Find the roots of the algebra expression

p_{1} = - \frac{4 822 2 ^{3}}{8222}, p_{2} = \frac{4 822 2 ^{3}}{8222}

Alternative Form

p_{1} \approx - 0.105016, p_{2} \approx 0.105016

Evaluate

p^{4} \times 8222 - 1

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

p^{4} \times 8222 - 1 = 0

Use the commutative property to reorder the terms

8222 p^{4} - 1 = 0

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

8222 p^{4} = 0 + 1

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

8222 p^{4} = 1

Divide both sides

\frac{8222 p ^{4}}{8222} = \frac{1}{8222}

Divide the numbers

p^{4} = \frac{1}{8222}

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

p = \pm 4 \frac{1}{8222}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8222}

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

\frac{4 1}{4 8222}

Simplify the radical expression

\frac{1}{4 8222}

Multiply by the Conjugate

\frac{4 822 2 ^{3}}{4 8222 \times 4 822 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

48222 \times 4 822 2^{3}

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

4 8222 \times 822 2^{3}

Calculate the product

4 822 2^{4}

Reduce the index of the radical and exponent with 4

8222

\frac{4 822 2 ^{3}}{8222}

p = \pm \frac{4 822 2 ^{3}}{8222}

Separate the equation into 2 possible cases

p = \frac{4 822 2 ^{3}}{8222} p = - \frac{4 822 2 ^{3}}{8222}

Solution

p_{1} = - \frac{4 822 2 ^{3}}{8222}, p_{2} = \frac{4 822 2 ^{3}}{8222}

Alternative Form

p_{1} \approx - 0.105016, p_{2} \approx 0.105016

Show Solution