Solve p^41728-1 - ScanMath

Pergunta

Simplify the expression

Solution

1728 p^{4} - 1

Evaluate

p^{4} \times 1728 - 1

Solução

1728 p^{4} - 1

Mostrar solução

Find the roots of the algebra expression

p_{1} = - \frac{4 10 8 ^{3}}{216}, p_{2} = \frac{4 10 8 ^{3}}{216}

Alternative Form

p_{1} \approx - 0.155101, p_{2} \approx 0.155101

Evaluate

p^{4} \times 1728 - 1

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

p^{4} \times 1728 - 1 = 0

Use the commutative property to reorder the terms

1728 p^{4} - 1 = 0

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

1728 p^{4} = 0 + 1

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

1728 p^{4} = 1

Divide both sides

\frac{1728 p ^{4}}{1728} = \frac{1}{1728}

Divide the numbers

p^{4} = \frac{1}{1728}

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

p = \pm 4 \frac{1}{1728}

Simplify the expression

Mais Passos

Evaluate

4 \frac{1}{1728}

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

\frac{4 1}{4 1728}

Simplify the radical expression

\frac{1}{4 1728}

Simplify the radical expression

Mais Passos

Evaluate

41728

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 108

Write the number in exponential form with the base of 2

4 2^{4} \times 108

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 4108

Reduce the index of the radical and exponent with 4

24108

\frac{1}{2 4 108}

Multiply by the Conjugate

\frac{4 10 8 ^{3}}{2 4 108 \times 4 10 8 ^{3}}

Multiply the numbers

Mais Passos

Evaluate

24108 \times 4 10 8^{3}

Multiply the terms

2 \times 108

Multiply the terms

216

\frac{4 10 8 ^{3}}{216}

p = \pm \frac{4 10 8 ^{3}}{216}

Separate the equation into 2 possible cases

p = \frac{4 10 8 ^{3}}{216} p = - \frac{4 10 8 ^{3}}{216}

Solução

p_{1} = - \frac{4 10 8 ^{3}}{216}, p_{2} = \frac{4 10 8 ^{3}}{216}

Alternative Form

p_{1} \approx - 0.155101, p_{2} \approx 0.155101

Mostrar solução